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In the ﬁgure below, If the area of triangle CDE is 42, what [#permalink]
Expert's post
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 [ 10.08 KiB | Viewed 15241 times ]

[Reveal] Spoiler: OA
378

Math Review
Question: 9
Page: 260
Difficulty: medium

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Re: In the ﬁgure below, If the area of triangle CDE is 42, what [#permalink]
3
KUDOS
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

[Reveal] Spoiler: OA
378

Math Review
Question: 9
Page: 260
Difficulty: medium

Here,
all the three triangles ( $$\triangle$$CDE , $$\triangle$$ BDF and $$\triangle$$ ADG are similar)

and one side of the $$\triangle$$ CDE = $$\frac{1}{3}$$of the $$\triangle$$ ADG

Hence the Area of $$\triangle$$ADG = $$(\frac{1}{2} * AG * DG) = (\frac{1}{2} * 3CE * 3DE) = 9 * (\frac{1}{2} * CE * DE)$$ = 9 * Area of the $$\triangle$$ CDE = $$9 * 42 = 378$$
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Re: In the ﬁgure below, If the area of triangle CDE is 42, what [#permalink]
3
KUDOS
Expert's post
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

[Reveal] Spoiler: OA
378

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 42
Area of triangle = (base)(height)/2
So, we can write: (y)(x)/2 = 42
This means: yx = 84

Area of triangle = (base)(height)/2
So, the area of ∆ADG = (3y)(3x)/2
= 9yx/2

Since we know that yx = 84, we can replace yx with 84 to get:
Area of ∆ADG = 9(84)/2 = 378

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com  Re: In the ﬁgure below, If the area of triangle CDE is 42, what   [#permalink] 29 May 2019, 07:55
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