The leg of a rectangular triangle refers to the hypotenuse as 5 to 13 find the perimeter of the triangle

The leg of a rectangular triangle refers to the hypotenuse as 5 to 13 find the perimeter of the triangle if the second leg is 24 cm.

Let us denote the unknown leg by the letter x, and the hypotenuse by the letter y.

Then, by the condition of the problem, we get:

x / y = 5/13,

y = 13 * x / 5.

Since the second leg is 24 cm, we draw up an equation using the Pythagorean theorem:

x² + 24² = (13 * x / 5) ²,

24² = 169 * х² / 25 – 25 * х² / 25,

24² = 144 * х² / 25,

24 = 12 * x / 5,

x = 24 * 5/12,

x = 10.

So y = 13 * 10/5 = 26.

Thus, the sides of the triangle are 10, 24 and 26 cm.

Therefore, the perimeter of the triangle is:

10 + 24 + 26 = 60 cm.

Answer: 60 cm.