Question

The hypotenuse of a right triangle is 13cm long. the longer leg is 7 cm longer than the shorter leg. find the side lengths of the triangle.

Answer 1

$5^2 + 12^2 = 13^2$

is the second or third Pythagorean triple on the list, which gives us the answer directly.

But if we didn't know that, let x be the short leg:

$x^2 + (x+7)^2 = 13^2$

$2x^2 + 14 x + 49 - 169 = 0$

$x^2 + 7x - 60 = 0$

$(x+12)(x-5)=0$

Rejecting the negative root, x=5, other side 12, the Pythagorean triple we found.