# 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 Δ*BCF* 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 .