You did pretty well last week explaining that problem! This week you need to find the answer AND explain why. Look at the picture below. ABE, BFE, and DBC are right triangles (with the right angles at B and F. What can I put in for x, y, and z so that the picture will work? Also, what's the area of quadrilateral ABFE?
Remember, no explanation, no credit!
Annie says: Solutions
A list of all the people who got this problem right follows the highlighted solutions below, and most of the solutions are also available.
The following students submitted correct solutions this week:
C. J. B., Grade 10, SI
Kasturi Chitnis, Grade 8, The Indian High School, Dubai, United Arab Emirates
Katsu Sato, Grade 6, Troy Intermediate School, Avon Lake, Ohio
David Choi, Grade 9, Marple Newtown Senior High School, Newtown Square, Pennsylvania
Aaron Bartley, Grade 9, Southeast Raleigh High School, Raleigh, North Carolina
Tim Chernock, Grade 6, Troy Intermediate School, Avon Lake, Ohio
Worawat Meevasana, Grade 12, The Mercersburg Academy, Mercersburg, Pennsylvania
David Shaw, Grade 9, Smoky Hill High School, Aurora, Colorado
Arnaldo Alvarez and Matt Hazel, Grade 8, Saint Gregory
Sumith Madhavarapu and Neil Crittenden, Grade , Casady School, Oklahoma City, Oklahoma
Matthew Hiatt, Grade 9, Smoky Hill High School, Aurora, Colorado
Robbie Boyle and Chris Bronson, Grade 9, 10, Granada High School, Livermore, California
John Allen, Grade 8, Louis Pasteur Middle School, Orangevale, California
Gordon Bockus Jr., Grade Freshman, Eastern Oklahoma State College, Wilburton, Oklahoma
Tiffanie Lam, Grade 8, Sequoia Middle School, Pleasant Hill, California
Stephen Oesterreich, Grade 6, Troy Intermediate School, Avon Lake, Ohio
Todd Sanders, Grade 9, Carlisle High School, Carlisle, Pennsylvania
Laura Smith, Grade 9, Bexley High School, Bexley, Ohio
Michael Hang, Grade 7, Arab High School, Arab, Alabama
Nihar Shah, Grade 8, Albright Middle School, Houston, Texas
Eve Levinson, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Stephen Nolen, Grade 9, Smoky Hill High School, Aurora, Colorado
Frank Cerros, Grade 9, Amador Valley High School, Pleasanton, California
Rick McCarthy, Grade 9, St. John Bosco High School, Bellflower, California
Jake Nelson, Grade 9, Smoky Hill High School, Aurora, Colorado
Mark Kaye, Grade 10, Smoky Hill High School, Aurora, Colorado
Emily Castor, Grade 9, Granada High School, Livermore, California
Kamila Sikora, Grade 9, Smoky Hill High School, Aurora, Colorado
Kasey Jones, Grade , Redmond High School, Redmond, Oregon
Laura Roos, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Barbara van Santen, Grade 9, American Embassy School, New Delhi, India
Roger Dieterich III, Grade 10, Smoky Hill High School, Aurora, Colorado
Aya Koshinaka, Grade 9, American Embassy School, New Delhi, India
Keith Clayton, Grade , Redmond High School, Redmond, Oregon
Grigoriy Syrkin, Grade 11, Malden High School, Masachusetts
Jared Bower, Grade 9, Franklin County High School, Rocky Mount, Virginia
Bridgette Ellis, Grade 9, Franklin County High School, Rocky Mount, Virginia
Jonathan Emmons and Amey Adkins, Grade 9, Franklin County High School, Rocky Mount, Virginia
Pal Randhawa, Grade 9, Casady School, Oklahoma City, Oklahoma
Margaret Osbourne, Grade 10, Washington County High School, Springfield, Kentucky
Jacob Ornelas, Grade , Smoky Hill High School, Aurora, Colorado
Matthew Jahnke, Grade 4, Northview Elementary School
Tanya Colburn, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania
Natalie Lauderdale, Grade , Redmond High School, Redmond, Oregon
Stevie King, Grade 9, Carlisle High School, Carlisle, Pennsylvania
Rebecca O'Connell, Grade , Redmond High School, Redmond, Oregon
Jessica Dougherty and Sarah Lawrence, Grade , Redmond High School, Redmond, Oregon
Ben Stewart, Grade , Redmond High School, Redmond, Oregon
Jennifer Au and Rachael Kun, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Brittney Mehring, Grade 9, Carlisle High School, Carlisle, Pennsylvania
Stevie King, Grade 9, Carlisle High School, Carlisle, Pennsylvania
Lauren Troutner, Grade 10, Smoky Hill High School, Aurora, Colorado
Arielle Cohen, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Josh Boyette, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Jackie Evans, Grade 9, Smoky Hill High School, Aurora, Colorado
Matt Niederst, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Vasanth Sriram, Grade 10, Academy of Allied Health and Science, Monmouth County, New Jersey
Laura Smith, Grade 9, Bexley High School, Bexley, Ohio
Lisa DeVita, Grade 9, Greenwich High School, Greenwich, Connecticut
Catalina Anghel, Grade , Mackenzie High School, Deep River, Ontario, Canada
David Patterson, Grade 10, St. John Bosco High School, Bellflower, California
Emmanuel Diaz, Grade 10, Greenwich High School, Greenwich, Connecticut
Brett Gadd, Grade 10, Amador Valley High School, Pleasanton, California
Saurabh Sarkar, Grade 8, Albright Middle School, Houston, Texas
Charlie Wenger, Grade 8, Odle Middle School, Bellevue, Washington
Bradley Hamilton, Grade 10, Washington County High School, Springfield, Kentucky
John Culver, Grade 10, Washington County High School, Springfield, Kentucky
Robert Osbourne, Grade 10, Washington County High School, Springfield, Kentucky
Steven Fogt, Grade 10, Washington County High School, Springfield, Kentucky
Katy Towles and Christian Curtian, Grade 10, Casady School, Oklahoma City, Oklahoma
Jared Settles, Grade 10, Washington County High School, Springfield, Kentucky
Erika Brackenbrough, Grade , Redmond High School, Redmond, Oregon
Danielle Lytle, Grade , Redmond High School, Redmond, Oregon
Benjamin Kloss, Grade , Redmond High School, Redmond, Oregon
Jen Erhart, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Mary Diamond and Mary Kenney, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania
Scott Steinbaugh, Grade 10, Fort Vancouver High School, Vancouver, Washington
Marcus Medina, Grade 10, St. John Bosco High School, Bellflower, California
Aaron Mertz, Grade 8, Plum Grove Junior High School, Rolling Meadows, Illinois
Oscar Robledo, Grade 10, St. John Bosco High School, Bellflower, California
Noam Abrams, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Brian Kim, Grade 10, Monterey Bay Academy, Watsonville, California
Kristen Meadows, Grade 11, Monterey Bay Academy, Watsonville, California
Neil Seifried, Grade 10, Pullman High School, Pullman, Washington
Roxanna Hamilton, Grade 11, Washington County High School, Springfield, Kentucky
Kareem Farooq, Grade 9, St. John Bosco High School, Bellflower, California
Patrick Draper, Grade 9, Normal Community West High School, Normal, Illinois
Mary Hansen, Grade 9, Smoky Hill High School, Aurora, Colorado
Paul McKenzie, Grade 10, Waubonsie Valley High School, Aurora, Illinois
Lisa Simmons, Grade , Redmond High School, Redmond, Oregon
Ben and Dallas Witty and Billy Miller, Grade , Redmond High School, Redmond, Oregon
Adrienne Ruegg, Grade , Carlisle High School, Carlisle, Pennsylvania
Allison Charnock, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Michael Maynes, Grade 10, St. John Bosco High School, Bellflower, California
Alex Svirsky, Grade 9, Smoky Hill High School, Aurora, Colorado
Gagan Nanda, Grade 11, Raffles Junior College, Singapore
Aviva Kremer, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Chad Medley, Grade 11, Washington County High School, Springfield, Kentucky
Joe David Smith, Grade 10, Washington County High School, Springfield, Kentucky
Eric Coulter, Grade 10, Washington County High School, Springfield, Kentucky
Perry Cottrell, Grade 9, Smoky Hill High School, Aurora, Colorado
Kristen Allegue, Grade 9, Ethel Walker School, Simsbury, Connecticut
Jerry Bartley, Grade 11, Washington County High School, Springfield, Kentucky
Tom O'Malley, Grade Staff, Willows High School, Willows, California
Adrian Yepez, Grade 10, St. John Bosco High School, Bellflower, California
Paul Parker, Grade Office, None
Cody Stagner, Grade 10, Washington County High School, Springfield, Kentucky
Gavin McClintock, Grade 9, Monterey Bay Academy, Watsonville, California
Mitsunori Tanabe, Grade 11, Monterey Bay Academy, Watsonville, California
Scott Coulter, Grade 10, Washington County High School, Springfield, Kentucky
Caleb Ho, Grade 11, Monterey Bay Academy, Watsonville, California
Paul Carney, Grade 10, Washington County High School, Springfield, Kentucky
Crystal Cannaday, Grade 9, Franklin County High School, Rocky Mount, Virginia
Meredith Cloyd , Grade 11, Washington County High School, Springfield, Kentucky
Alyson Spalding, Grade 10, Washington County High School, Springfield, Kentucky
John Martin, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Brian Lukoff, Grade 10, Germantown Friends School, Philadelphia, Pennsylvania
Jason Mattingly, Grade 10, Washington County High School, Springfield, Kentucky
Derek Terrell, Grade 10, Washington County High School, Springfield, Kentucky
Alan Hoffman, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois
Jenny Weinbaum, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois
Tim Lewis, Grade 8, Owen J. Roberts Middle School, Pottstown, Pennsylvania
Dragan Plakalovic, Grade 10 , Durango High School
Michael Steven, Grade 10, St. John Bosco High School, Bellflower, California
Jeff Knepper, Grade 10, Smoky Hill High School, Aurora, Colorado
Ryan Seng, Grade 10, Granada High School, Livermore, California
Kristi Coady, Grade 9, Smoky Hill High School, Aurora, Colorado
Natasha Fedner, Grade 9, Bexley High School, Bexley, Ohio
Dan McCoy, Grade 9, Marple Newtown Senior High School, Newtown Square, Pennsylvania
Travis Mandala, Grade 10, St. John Bosco High School, Bellflower, California
Autumn N. and Lindsay R. and Abby M, Grade 6, Troy Intermediate School, Avon Lake, Ohio
Jason Slomovitz, Grade 9, The Hun School of Princeton, Princeton, New Jersey
Emily Lu, Grade 9, Granada High School, Livermore, California
Aaron Streza, Grade 6, Troy Intermediate School, Avon Lake, Ohio
Philip Deary, Grade 10, St. John Bosco High School, Bellflower, California
Cliff Harski, Grade 10, American Embassy School, New Delhi, India
Jenna Kim, Grade 6, Lemon Road Elementary School, Falls Church, Virginia
Ricardo Villalobos, Grade 10, St. John Bosco High School, Bellflower, California
Bradley Hamilton, Grade 10, Washington County High School, Springfield, Kentucky
Jason Sturgell and Tony Altomare, Grade 12 , Columbiana County Career Center, Lisbon, Ohio
Jessica Barclay-Strobel, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois
Nyla Walker, Grade 10, Shelby County High School, Columbiana, Alabama
Jeffrey Kilheffer, Grade 9, Carlisle High School, Carlisle, Pennsylvania
Laurie Spalding, Grade 10, Washington County High School, Springfield, Kentucky
Alicia Osbourne, Grade 10, Washington County High School, Springfield, Kentucky
Teneal Dollar, Grade 10, Shelby County High School, Columbiana, Alabama
Justin Drummonds, Grade , Smoky Hill High School, Aurora, Colorado
Brian Fallis, Grade 10, Washington County High School, Springfield, Kentucky
Tammy Davis, Grade 11, Shelby County High School, Columbiana, Alabama
Kelly Barnes, Grade 10, Washington County High School, Springfield, Kentucky
Tony Filiatreau, Grade 11, Washington County High School, Springfield, Kentucky
Adrian Lai, Grade , Salesian School, Hong Kong
Erika Mitchell, Grade 11, Shelby County High School, Columbiana, Alabama
Chris Jones, Grade 10, Shelby County High School, Columbiana, Alabama
Karly Hendrix, Grade 9, Smoky Hill High School, Aurora, Colorado
Jason Wilkins, Grade 11, Shelby County High School, Columbiana, Alabama
Justin Dembowski, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Abbie Rowley and Brie Compton, Grade 10, Mount Saint Joseph Academy, Flourtown, Pennsylvania
Rob Sim, Grade 10, Middletown High School North, Middletown, New Jersey
Rudolf Vlk, Grade 10, St. John Bosco High School, Bellflower, California
Robert Boismier, Grade 10, Monterey Bay Academy, Watsonville, California
Brandon Unger, Grade 10, St. John Bosco High School, Bellflower, California
Meredith Blackman, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Lora Coleman, Grade 11, Shelby County High School, Columbiana, Alabama
Daisuke Kojima, Grade , American Embassy School, New Delhi, India
Sohil Tuladhar, Grade 11, American Embassy School, New Delhi, India
Erin Roll, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Sarah and Shaun Lindquist and Burdett, Grade , Redmond High School, Redmond, Oregon
Jack Boegel, Grade 12, Livermore High School, Livermore, California
Kim McBride, Grade , Redmond High School, Redmond, Oregon
Shameica Edwards, Grade 12, Wingate High School, Brooklyn, New York
Keisha Paul, Grade 10, Wingate High School, Brooklyn, New York
My Nhia Lee, Grade 9, Highland Park Senior High School, St. Paul, Minnesota
Emily Chisholm, Grade , Redmond High School, Redmond, Oregon
Clint Soose, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Brandi Marsh, Grade 9, Ethel Walker School, Simsbury, Connecticut
Noelle Rentsch, Grade , American Embassy School, New Delhi, India
Robert Revay, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Heather Nellis, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Lemecha' Bush, Grade 12, Shelby County High School, Columbiana, Alabama
Kelly Dorsch, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Emily Demich, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Nick Watts, Grade , Redmond High School, Redmond, Oregon
Jill Filipovitz, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Joel Jorgensen, Grade , Redmond High School, Redmond, Oregon
Emily Schuler, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Kimberly Woodall, Grade 10, Shelby County High School, Columbiana, Alabama
Robin Thornburg, Grade 11, Shelby County High School, Columbiana, Alabama
Dale Fortenberry, Grade 10, Shelby County High School, Columbiana, Alabama
Jon Gantman, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
April Sjoboen, Grade 11, Monterey Bay Academy, Watsonville, California
Allen Kuo, Grade 9, Granada High School, Livermore, California
Sergio Vasquez, Grade 10, St. John Bosco High School, Bellflower, California
Christina Lewis, Grade 10, Washington County High School, Springfield, Kentucky
Josh Taft, Grade , Smoky Hill High School, Aurora, Colorado
Jim Nguyen, Grade 9, Smoky Hill High School, Aurora, Colorado
Mathew Steadman, Grade 8, Odle Middle School, Bellevue, Washington
Wassia Khaja, Grade 8, Albright Middle School, Houston, Texas
Sarah Stoenner, Grade 9, Southeast Raleigh High School, Raleigh, North Carolina
Alaina Hollis, Grade 10, Smoky Hill High School, Aurora, Colorado
June Lin, Grade 5, Sahuaro Elementary School, Tuscon, Arizona
Hannah Margoles, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Tom Miles and Scott Gauweiler, Grade 10, Northwestern Lehigh High School, New Tripoli, Pennsylvania
Jenny Kaplan, Grade 7, Castilleja Middle School, Palo Alto, California
Blake Schaub, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Chris Lauber, Grade 9, Smoky Hill High School, Aurora, Colorado
Natko Bajic, Grade 7, Pojisan Primary School, Split, Croatia
Hunter Brooks, Grade 8, Camelot Academy, Durham, North Carolina
Andrea Medini, Grade , A. Righi, Italy
Sari Yehuda, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Simon Porzak, Grade 7, The Academy
Jenny Lurie, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Richard Balsley, Grade 10, Granada High School, Livermore, California
Stacie Graham, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Heather Beck, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Eric Dubas, Grade , Germantown Academy, Fort Washington, Pennsylvania
Zimran Douglas, Grade 12, Wingate High School, Brooklyn, New York
Ryan Holcomb, Grade , Redmond High School, Redmond, Oregon
Darrin Koski and Trent Ludwig and Joel Smith and Kendra Cutter, Grade , Redmond High School, Redmond, Oregon
Pete Darnell, Grade , Redmond High School, Redmond, Oregon
Jason Chiu, Grade 9, Laramie Junior High School, Laramie, Wyoming
Tou Lee, Grade 10, Highland Park Senior High School, St. Paul, Minnesota
Avrum Tilman, Grade , Akiba Hebrew Academy, Merion, Pennsylvania
Abin Bandy, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Matt Smawfield, Grade 9, American Embassy School, New Delhi, India
Dan Resnick and Jeff Beer, Grade 9, Germantown Academy, Fort Washington, Pennsylvania
Chris Adamiak, Grade 10, Amador Valley High School, Pleasanton, California
Alex Morgovsky, Grade 11, Akiba Hebrew Academy, Merion, Pennsylvania
Darian Allen and Kevin Beyer, Grade 10, Northwestern Lehigh High School, New Tripoli, Pennsylvania
Houman Ebrahimi, Grade 12, Carlingford High School, Australia
Kyle Fort, Grade 10, Pullman High School, Pullman, Washington
Sijin Joseph, Grade Undergraduate, St. Stephen's College, India
THE GENIUS, Grade 9, International School of Choueifat, Dubai
Jeff Burlin, Grade 9, Southeast Raleigh High School, Raleigh, North Carolina
David Grant, Grade , Livermore High School, Livermore, California
Mike Nollen, Grade ,
Shantel Naylor, Grade 9, Granada High School, Livermore, California
Alex Chen, Grade 7, Odle Middle School, Bellevue, Washington
Michelle Wagner, Grade , Mount Saint Joseph Academy, Flourtown, Pennsylvania
Chris Mize, Grade 9, Southeast Raleigh High School, Raleigh, North Carolina
Crista Petrelli, Grade 9, Greenwich Academy, Greenwich, Connecticut
Megan Via, Grade 9, Franklin County High School, Rocky Mount, Virginia
Sonia Teas, Grade 10, Oak Park and River Forest High School, Oak Park, Illinois
Kelly Flis, Grade 10, Shaler Area High School, Pittsburgh, Pennsylvania
Frannie Laks, Grade 10, Akiba Hebrew Academy, Merion, Pennsylvania
Melanie, Grade 9, Skyview High School, Vancouver, Washington
Robert Murray, Grade 10, Kenny Lake School, Copper Center, Alaska
Brian Bairstow, Grade , Mount Whitney High School, Visalia, California
Melissa Hackel, Grade , Granada High School, Livermore, California
Emily Rozak, Grade , Germantown Academy, Fort Washington, Pennsylvania
Mike Buckler and T.J. Wudarski, Grade , Germantown Academy, Fort Washington, Pennsylvania
Jennifer Liang, Grade 8, Odle Middle School, Bellevue, Washington
Jennifer, Grade , Granada High School, Livermore, California
Nathan Reynolds, Grade 9, Franklin County High School, Rocky Mount, Virginia
Anne Hines and Lauren Rossi, Grade 10, Germantown Academy, Fort Washington, Pennsylvania
Zach Dillon, Grade 7, Odle Middle School, Bellevue, Washington
Robt M., Grade ,
Jordie Kvidera, Grade 7, Odle Middle School, Bellevue, Washington
Travis Guy, Grade , Redmond High School, Redmond, Oregon
Michelle Peterson and Katie McDonald, Grade , Redmond High School, Redmond, Oregon
Ikechukwu Njoku, Grade 11, Wingate High School, Brooklyn, New York
Casey Sutherland, Grade , Redmond High School, Redmond, Oregon
Jody Rogers and Conor Ferguson and Ryan Tesconi, Grade , Redmond High School, Redmond, Oregon
Greg Alway, Grade , Redmond High School, Redmond, Oregon
Nate Hodnefield, Grade , Redmond High School, Redmond, Oregon
Andrew Cooledge, Grade 7, Odle Middle School, Bellevue, Washington
Deanna Smith, Grade , Redmond High School, Redmond, Oregon
Mike Montreuil, Grade , Redmond High School, Redmond, Oregon
Jason Gides, Grade , Shaler Area High School, Pittsburgh, Pennsylvania
Victoria Soto, Grade 10, Monterey Bay Academy, Watsonville, California
Mary Park, Grade 8, Odle Middle School, Bellevue, Washington
Maja White, Grade 9, Highland Park Senior High School, St. Paul, Minnesota
Alex Chernyavsky, Grade , Akiba Hebrew Academy, Merion, Pennsylvania
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