The lengths of the corresponding sides of 2 similar right triangles are in the ratio of 2: 5. if the hypotenuse of the smaller triangle is 5 inches long, how many inches long is the hypotentuse of the larger triangle?

Since the ratio is 2:5, it could be written as a fraction: 2/5. To make this apply to the sides of the triangles you'd have to create an equation where 2/5 equals 5/x, x being the length of the hypotenuse.

2/5 = 5/x

To get from 2 to 5, you'd have to multiply 2 by 2.5. Therefore, in order to make the equation equal, you have to multiply 5 (the denominator of 2/5) by 2.5.

2/5 = 5/12.5

The hypotenuse would be 12.5 inches long.