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Problem Solving (PS) | In the figure above, if triangles ABC, ACD, and ADE are isosceles righ

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BrentGMATPrepNow wrote:

Bunuel wrote:
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In the figure above, if triangles ABC, ACD, and ADE are isosceles right triangles and the area of ΔABC is 6, then the area of ΔADEis

A. 18
B. 24
C. 36
D. \(12\sqrt{2}\)
E. \(24\sqrt{2}\)


In general, isosceles right triangles have the following properties.
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Notice that the hypotenuse = (√2)(length of oneleg)

So, let's label the sides of the BLUE triangle asfollows:
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This means each leg of the RED triangle has length (√2)(x)
Image


The hypotenuse of an isosceles right triangle = (√2)(length of one leg) . . .
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. . . so the length of the hypotenuse = (√2)(√2)(x) =2x


This means each leg of the GREEN triangle has length 2x
Image


What is the area ofΔADE?

Area of triangle =(base)(height)/2
...

Statistics : Posted by Kimberly77 • on 26 Apr 2019, 05:26 • Replies 12 • Views 18975



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