The perimeter of a right-angled triangle is 24 cm, and one of the legs is 6 cm. find the second leg and hypotenuse.

Knowing the size of one leg and the perimeter of the triangle, we find the sum of the second leg and the hypotenuse: 24 – 6 = 18 (cm). Let the hypotenuse of the triangle be x (x) cm, then the second leg – (18 – x) cm.Knowing the values of the legs and the hypotenuse, we apply the Pythagorean theorem and compose the equation:
(18 – x) ² + 6² = x²;
324 – 36 • x + x² + 36 – x² = 0;
– 36 • x = – 360;
x = 360: 36;
x = 10 (cm) – the hypotenuse of the triangle;
18 – x = 18 – 10 = 8 (cm) – second leg.
Answer: the hypotenuse of the triangle is 10 cm, the second leg is 8 cm.