One leg of a right triangle has a length of 7 m. the other sides have lengths that are consecutive integers. find these lengths

Let's make an equation based off of the pythagorean theorem.

7²+x² = (x+1) ²

Since the diagonal is the biggest of the three lengths, the diagonal is the bigger even number. Since they are consecutive, they are one away. Let's distribute.

49+x²=x²+2x+1; let's subtract 1 from both sides.

48+x²=x²+2x; lets subtract x² from both sides.

48=2x; let's divide.

48:2=24=x

So, since smaller integer is 24, the bigger one is 25. Let's make sure this makes sense.

7²+24²=25²

49+576=625

625=625

So, the missing lengths are 24 and 25.