The correct answer is (E).
Getting to the Answer: Use the 2:5 ratio of the side lengths of the two similar triangles to set up the proportion 2⁄5=5⁄h, where h is the length of the hypotenuse of the larger triangle. Cross multiply to get 2h = 25, and then divide both sides by 2 to see that h = 25⁄2 = 12.5.
(A) Incorrect: this is the result of inverting the ratio to obtain 2⁄5=h⁄5
(B) Incorrect: this is the result of dividing the length of the shorter hypotenuse (5) by 2
(C) Incorrect: this is the result of adding 2 + 5 = 7
(D) Incorrect: this is the result of multiplying 2 x 5 = 10
(E) Correct: this matches the correct calculation