One of the legs of a right-angled triangle is 9 cm, and the hypotenuse is 3 cm larger

One of the legs of a right-angled triangle is 9 cm, and the hypotenuse is 3 cm larger than the second leg. Find the perimeter of the rectangle.

By the Pythagorean theorem:

c² = a² + b², where a and b are the legs of a right-angled triangle, c is its hypotenuse;

a = 9 cm; c = b + 3;

(b + 3) ² = a² + b²; b² + 2 b * 3 + 3² = a² + b²;

6 b = a² – 9 = 9² – 9 = 72 (cm²); b = 72: 6 = 12 (cm);

c = 12 + 3 = 15 (cm);

The perimeter of a triangle is equal to the sum of all its sides:

P = a + b + c = 9 + 12 + 15 = 36 (cm).