hypotenuse question

Question

A right triangle has leg lengths of 18 and 24 and a hypotenuse of 15n. What's the value of n?

Answer 1

18 = 3(6), 24 = 4(6), so hypotenuse must be 5(6)...similarity to 3-4-5- rt. triangle.

Therefore 30 = 15n so n = 2.