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Picture Frame, Triangle Measurements

Date: 5/20/96 at 3:21:9
From: Anonymous
Subject: Quadratic equations

My teacher gave us 10 questions to answer and I could do all of
them except two:

1) A framed rectangular picture is 35cm long and 25cm wide. The area 
of the picture itself is 375cm squared. How far is it from the edge of 
the frame to the edge of the picture if this width is uniform around 
the picture?

2) The base of a triangle is 9cm more than the perpendicular height. 
The area of the triangle is 200cm squared. What are the lengths of the 
base and the perpendicular height?

Date: 6/10/96 at 10:50:51
From: Doctor Darren
Subject: Re: Quadratic equations

On the first question one you need to start by getting a clear picture 
in your head.  You know that we are looking for the distance from the 
picture to the edge, let's call this value d.  Now we know that the 
picture is l centimeter long and w centimeters wide.  Thus, we have 
the following equations:

l+2d = 35
w+2d = 25
l*w = 375

Thus, l-w = 10.
so l*(l-10)=375, or l = 25, w = 15
so d = 5.

Does this make sense to you?

In the second question, we know that the formula for the area of a 
triangle is (1/2)bh.  In this problem we have that b = h+9.

Thus, (1/2)(h+9)h = 200
       h^2+9h-400 = 0
       h = (-9+SQRT(1681))/2=(-9+41)/2 = 16
 so b = 25

I hope this helped!

-Doctor Darren,  The Math Forum
 Check out our web site!   
Associated Topics:
High School Basic Algebra
High School Geometry
High School Triangles and Other Polygons

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