SAT Math Multiple Choice Practice Question 43: Answer and Explanation

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Question: 43

21.

Given that ABCD is a rectangle, and triangle BCF is isosceles, find the length of the line segment BE in this diagram.

A.
B.
C. 12
D.
E. 13

Correct Answer: E

Explanation:

E. Because triangle BCF is isosceles, BC = CF = 8. Because angle D is a right angle, triangle DEF is the world-famous 3-4-5 right triangle, and DF = 4. Because DC = 4 + 8 = 12, AB is also 12. And, because AD = BC = 8, AE = 8 - 3 = 5. Now you're ready to find EB, the hypotenuse of the right triangle ABE. You can, of course, use the Pythagorean Theorem, but you'll save time if you realize that you're face to face with a 5-12-13 right triangle, and BE = 13.

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