the hypotenuse of a right triangle has a length of 13cm the longer of the two legs is 7cm longer than the shorter leg

Let's say the shorter side is x.

So, the longer side would be (7 + x)

Now we have to use the Pythagorean Theorem to find the value of x.

a² + b² = c²

(7 + x) ² + x² = 13

7² + x² + x² = 13²

49 + 2x² = 169

2x² = 169 - 49

2x² = 120

x² = 60

x = √60

So the longer side is (7 + √60) and the shorter side is √60