SAT Math Multiple Choice Practice Question 379: Answer and Explanation

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Question: 379

5.

In the figure above, the vertices of square EFGH are on the diagonals of square ABCD. If and what is the sum of the lengths (heavier lines)?

A. 24
B. 28
C. 32
D. 36
E. 38

Correct Answer: A

Explanation:

A The sides of square EFGH all have length A diagonal of this square can be found with the Pythagorean theorem:

(Or, more simply, you can remember that the length of the diagonal of a 45°-45°-90° triangle is the length of the side times So the diagonal is ) By the same reasoning, since the sides of square ABCD all have length

Notice that ; therefore,, so . By the same reasoning,, so .

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