2014-10-08 09:00:50

Two right triangles are similar. One has sides of 10, 24, and 26. Which of the following could be the length of the hypotenuse of the the other triangle?

I. 13
II. 36
III. 65

(A) I only
(B) III only
(C) I and II
(D) I and III
(E) I, II, and III

The correct answer is D
Explanation: If the two triangles are similar, then their sides are proportional. The hypotenuse of a right triangle is its longest side, so the hypotenuse of the other triangle must be proportional to 26, meaning that it must have a common factor with 26. 13 is a common factor of 26, since both numbers are divisible by 13. Option I is correct, then. Similarly, option III works, since 65 and 26 both have 13 as a factor. 36 does not work, though, as 36 is proportional to 24, not 26. Thus, option II does not work. Since I and III do, choice D is correct.