Question

The shortest side of a right triangle measures 7 m. the lengths of the other two sides are consecutive integers​ - the hypotenuse being the longer of the two. find the lengths of the other two sides.

Answer 1

If the lengths of the other two sides are consecutive integers, then the second leg is n and the hypotenuse is n+1. By the Pythagorean theorem:

$(\text{hypotenuse})^2=(\text{leg}_1)^2+(\text{leg}_2)^2,\\ (n+1)^2=n^2+7^2,\\ n^2+2n+1=n^2+49,\\ 2n+1=49,\\ 2n=48,\\ n=24$

and

n+1=25.

Answer: the unknown sides have lengths 24 and 25.