Picture Frame, Triangle MeasurementsDate: 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! http://mathforum.org/dr.math/ |
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