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