SAT Math Multiple Choice Practice Question 189: Answer and Explanation

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Question: 189

13. The diagonal of a rectangle is twice as long as its width. If the width of the rectangle is represented as x, what is the area of the rectangle, in terms of x?

A.
B. x2
C.
D.
E. 2x2

Correct Answer: D

Explanation:

D. Drawing a picture for this problem is a good idea.

If you don't immediately recognize this as a 30°-60°-90° triangle, you can use the Pythagorean Theorem to find the third side of the right triangle formed by the diagonal (which will be the length of the rectangle). For the moment, call the length of the rectangle a. Plugging into the Pythagorean Theorem, a2 + x2 = (2x)2 simplifies to a2 + x2 = 4x2, or a2 = 3x2. You take the square root of both sides and get . Now that you know the length of the rectangle, you can find the area by multiplying the length by the width: , Choice (D).

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