Carcass wrote:

In the ﬁgure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG?

Attachment:

#GREexcercise In the ﬁgure below, If the area of triangle CDE is 42, what is AB=BC=CD..jpg

Math Review

Question: 9

Page: 260

Difficulty: medium

Let's add the given information to the diagram.

Notice that the angles (represented by blue dots) are all equal.

If we draw some auxiliary lines from points B and C....

...we find that we have 3 IDENTICAL right triangles

If we let y = the base of ∆CDE and let x = the height of ∆CDE...

...then we can add several more x's and y's to the diagram.

From this, we can see that...

...the base of ∆ADG has length 3y and a height of 3x

GIVEN: the area of ∆CDE is 42Area of triangle = (base)(height)/2

So, we can write: (y)(x)/2 = 42

This means:

yx = 84We're asked to find the area of ∆ADG

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

So, the area of ∆ADG = (3y)(3x)/2

= 9

yx/2

Since we know that

yx = 84, we can replace

yx with

84 to get:

Area of ∆ADG = 9(

84)/2 = 378

Answer: 378

Cheers,

Brent

_________________

Brent Hanneson – Creator of greenlighttestprep.com

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