The perimeter of a right-angled triangle is 24 cm. The hypotenuse of the triangle is 4 cm less than the sum of its legs.

The perimeter of a right-angled triangle is 24 cm. The hypotenuse of the triangle is 4 cm less than the sum of its legs. One of the legs is 2 cm longer than the other. Find the length of each leg of the triangle.

Let x be one leg, then x + 2 is the second leg.
(x + x + 2) -4 is the hypotenuse.
Since the perimeter is the sum of the lengths of all sides, we can make an equation.
x + x + 2 + (x + x + 2) -4 = 24
4x + 4-4 = 24
4x = 24
x = 6-length of the first leg
6 + 2 = 8-length of the second leg