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In the figure below, If the area of triangle CDE is 42, what
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26 May 2019, 01:46
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?
#GREexcercise In the figure below, If the area of triangle CDE is 42, what is AB=BC=CD..jpg [ 10.08 KiB | Viewed 52590 times ]
Attachment:
#GREexcercise In the figure below, If the area of triangle CDE is 42, what is AB=BC=CD..jpg [ 10.08 KiB | Viewed 52590 times ]
Show: :: OA
378
Math Review
Question: 9
Page: 260
Difficulty: medium
Question: 9
Page: 260
Difficulty: medium
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Re: In the figure below, If the area of triangle CDE is 42, what
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29 May 2019, 07:55
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
Show: :: OA
378
Math Review
Question: 9
Page: 260
Difficulty: medium
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
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
General Discussion
Re: In the figure below, If the area of triangle CDE is 42, what
[#permalink]
26 May 2019, 19:20
26 May 2019, 19:20
6
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
Show: :: OA
378
Math Review
Question: 9
Page: 260
Difficulty: medium
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 = \(9 * 42 = 378\)
