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OG What is the length of a side of square region A

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AbeNeedsAnswers Master | Next Rank: 500 Posts
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OG What is the length of a side of square region A

Tue Aug 22, 2017 7:37 pm

In the figure above, if the area of triangular region D is 4, what is the length of a side of square region A ?

(1) The area of square region B is 9.
(2) The area of square region C is 64/9.

D

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Aug 28, 2017 2:41 pm

Since this is a DS question, we CANNOT trust the picture. We can trust any descriptions and numbers that we are given though - so we know that the triangle is a RIGHT triangle, it's area IS 4 and the shape A IS a square. We're asked for a side length of square A.

1) The area of square region B is 9.

Since shape B is a square - and its area is 9 - we know that its sides are each 3. Knowing the height of the triangle is 3, we can figure out its base:
Area = (1/2)(Base)(Height)
4 = (1/2)(B)(3)
4 = 1.5B
4/1.5 = B
With the base and the height, we CAN figure out the length of the diagonal (by using the Pythagorean Theorem), so we would have the answer to the question.
Fact 1 is SUFFICIENT

2) The area of square region C is 64/9.

While the information in Fact 2 might look a big 'weird', we know from the work that we did in Fact 1 that if we have either the base or the height of the triangle, then we can figure out the other side and then solve the diagonal. Thus, Fact 2 is also enough information to answer the question.
Fact 2 is SUFFICIENT

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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