SAT Math Multiple Choice Practice Question 450: Answer and Explanation

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Question: 450

12.

If the area of square ABFE = 25, and the area of BCF = 10, what is the length of ?

A. 7
B. 8
C. 9
D. 10
E. 14

Correct Answer: C

Explanation:

C First, you can estimate. Because square ABFE has an area of 25, EF equals 5 and EC looks to be a little less than twice EF, or in the 7–9 range. Thus, since CE = ED, because they are the legs of a 45?-45?-90? triangle, you can eliminate D and E. You also know that the area of ΔBCF is 10, and that its base (BF) is 5. Using the formula for area, you can calculate FC, the height of the triangle: 10 = (5) × (h), h = 4. So 5(FE) + 4(FC) = 9, which is the length of and .

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