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

24m and 25m.

Step-by-step explanation:

By Pythagoras Theorem:

h^2 = x^2 + 7 ^2       where h  is the hypotenuse and  x is the other leg.

But x and h are consecutive integers

so h = x + 1 and:

(x + 1)^2 = x^2 + 49

x^2  + 2x + 1 - x^2 = 49

2x + 1 = 49

2x = 48

x = 24

So the 2 lengths are 24 and 25.