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In the figure below, If the area of triangle CDE is 42, what

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In the figure below, If the area of triangle CDE is 42, what [#permalink] New post 26 May 2019, 01:46
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In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG?

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#GREexcercise In the figure below, If the area of triangle CDE is 42, what is AB=BC=CD..jpg
#GREexcercise In the figure below, If the area of triangle CDE is 42, what is AB=BC=CD..jpg [ 10.08 KiB | Viewed 1798 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] New post 26 May 2019, 19:20
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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] New post 29 May 2019, 07:55
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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.
Image


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


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


If we let y = the base of ∆CDE and let x = the height of ∆CDE...
Image
...then we can add several more x's and y's to the diagram.

From this, we can see that...
Image
...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


We're asked to find the area of ∆ADG
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

Answer: 378

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

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