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605-655 (Medium)|   Geometry|      
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Sajjad1994
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In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 11:18
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C
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45% (medium)

Question Stats:

67% (01:59) correct 33% (01:38) wrong based on 85 sessions

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In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

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C

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mikemcgarry
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In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 13:11
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SajjadAhmad
In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

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Dear SajjadAhmad,

I'm happy to respond. :-)

This is quite straightforward.
Attachment:
similar right triangles.png
similar right triangles.png [ 13.23 KiB | Viewed 6829 times ]
We know we have (angle ACB) = (angle AED) = 90 degrees.
We have AE = DE = 2, so the area of triangle ADE is 2.

The two triangles must be similar, because they share right angles and the angle at A. Because AE = DE, we know that AC = BC = 3/2.

The area of triangle ABC = (1/2)bh = (1/2)(3/2)(3/2) = 9/8

shaded region = (area of triangle ADE) - (area of triangle ABC) = 2 - 9/8 = 7/8

Answer = (C)

Does all this make sense?
Mike :-)
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Sajjad1994
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In the figure to the right, both triangles are right triangles. The ar 26 May 2017, 22:55
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mikemcgarry
SajjadAhmad
In the figure BELOW, both triangles are right triangles. The area of the shaded region is

(A) 1/2
(B) 2/3
(C) 7/8
(D) 3/2
(E) 5/2

Nova GMAT
Dear SajjadAhmad,

I'm happy to respond. :-)

This is quite straightforward.
Attachment:
similar right triangles.png
We know we have (angle ACB) = (angle AED) = 90 degrees.
We have AE = DE = 2, so the area of triangle ADE is 2.

The two triangles must be similar, because they share right angles and the angle at A. Because AE = DE, we know that AC = BC = 3/2.

The area of triangle ABC = (1/2)bh = (1/2)(3/2)(3/2) = 9/8

shaded region = (area of triangle ADE) - (area of triangle ABC) = 2 - 9/8 = 7/8

Answer = (C)

Does all this make sense?
Mike :-)
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Hi Mike

Thanks God you didn't say it is a bad quality question or non-GMAT type or Flawed Question :)
Thanks for Solution
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pushpitkc
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In the figure to the right, both triangles are right triangles. The ar 31 May 2017, 13:03
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Another way to do this question is as follows:

The shaded region comprises of both
a rectangle of dimensions 2- 3/2(1/2)(breadth) and 3/2(length) and
a triangle with dimensions 1/2(base) and 1/2(height).

The area for the rectangle is 3/4(3/2*1/2)
Similarly the area of the triangle is
(1/2)*(1/2)*(1/2) = 1/8

Added the sum for area of the shaded portion is 3/4 + 1/8 or 7/8(Option C)

Sent from my ONEPLUS A3003 using GMAT Club Forum mobile app
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VyshakhR1995
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In the figure to the right, both triangles are right triangles. The ar 31 May 2017, 13:28
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The triangles are similar.
Area of large on is 1/2*2*2
area of small one 1/2 *3/2 * 3/2
Shaded region = 2 - 9/8
7/8 is the answer
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zaidi1212
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In the figure to the right, both triangles are right triangles. The ar 08 Dec 2022, 10:11
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Area of the larger triangle: 2*2*1/2 = 2
Area of the smaller traingle: 1/2 * 3/2 * 3/2 = 9/8

Area of the shaded region = 2 - 3/8 = 16-9/8 = 7/8
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