The hypotenuse of a right-angled triangle is 52 cm and the legs are proportional to the numbers

The hypotenuse of a right-angled triangle is 52 cm and the legs are proportional to the numbers 5 and 12, find the perimeter.

By condition, triangle ABC is rectangular and the ratio of legs BC / AB = 5/12.

Then BC = AB * 5/12.

Let the length of the small leg be 5 * X, then the length of the larger leg will be 12 * X.

By the Pythagorean theorem, AC ^ 2 = AB ^ 2 + BC ^ 2.

52 ^ 2 = (5 * X) ^ 2 + (12 * X) ^ 2.

2704 = 25 * X ^ 2 + 144 * X ^ 2.

169 * X ^ 2 = 2704.

X ^ 2 = 2704/169 = 16.

X = 4.

Then AB = 5 * 4 = 20 cm.

BC = 12 * 4 = 48 cm.

The perimeter will be: P = 52 + 20 + 48 = 120 cm.

Answer: The perimeter of the triangle is 120 cm.