We know that the perimeter is 72 meters, so we have
Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:
Expand the squares to get
Bring everything to the right hand side to get
Divide both sides by 8:
This equation has solutions
This solutions would yield the following side lengths:
Since we can't have negative side lengths, we can only accept the solution x=9.
In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.