SAT Math Multiple Choice Practice Question 603: Answer and Explanation

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Question: 603

17.

In the figure above, ABCD is a rectangle. If YD = 4 and DZ = 3, what is the area of ABCD ?

A. 3
B. 7
C. 8
D. 16
E. 49

Correct Answer: D

Explanation:

D Label the figure with any information provided by the question. We know that YD = 4 and DZ = 3. First focus on triangle ADZ. Because we have an angle of 30° and a right angle symbol, we are working with a 30-60-90 triangle. The length of AD is the hypotenuse of the triangle and one of the dimensions we need to find the area of rectangle ABCD. The ratio of sides in triangle ADZ is x : x : 2x, where x is the length of the side opposite the 30° angle and 2x is the hypotenuse So AD = 2x = 6. To find the other dimension of the rectangle, look at triangle CYD. This too is a 30-60-90 triangle, ∠CDY = 30° because it forms a straight line with the 90° of the rectangle and the 60° from triangle ADZ. The question states that DY = 4, and this is opposite the 60° angle. Using the ratio, 4 = x, and , and the hypotenuse, CD, must be . Now we have enough information to find the area of the rectangle: . Multiply the top and bottom of the fraction by to get 16, as seen in answer D.

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