One leg of a right triangle has a length of 77 m. the other sides have lengths that are consecutive integers. find these lengths.

Let x and x+1 represent the consecutive integers, then x is the other leg and x+1 is the hypotenuse (because the hypotenuse must be greater than its sides).

Use Pythagorean Theorem:

a² + b² = c²

(77) ² + x² = (x+1) ²

5929 + x² = x² + 2x + 1

5928 = 2x

2964 = x

x+1 = 2965

Answer: The other leg is 2964 m and the hypotenuse is 2965 m