The legs of a right-angled triangle are 10 cm and 24 cm in the other rectangle.

The legs of a right-angled triangle are 10 cm and 24 cm in the other rectangle. hypotenuse and leg are 13 to 5. the ratio of the perimeters of these triangles is 2/3 find the sides of the second triangle

By the Pythagorean theorem, we will find the hypotenuse of the first right-angled triangle.

c = √ (10 * 10 + 24 * 24) = √ (100 + 576) = √676 = 26 cm.

Find the perimeter of the first triangle.

P = 10 + 24 + 26 = 60 cm.

Find the perimeter of the second triangle from the ratio.

60 / P2 = 2/3;
P2 = 60 * 3/2 = 90 cm.

We write the ratio of the hypotenuse and leg of the second triangle in the form:

c / a = 13/5.

c = 13 / 5a.

Let’s compose and solve the equation for the perimeter of the second triangle.

c + b + a = 90;
a + 13 / 5a + √ (13 / 5a) 2 – a2) = 90;
a + 13 / 5a + √ (169 – 25) / 25a2 = 90;

5 / 5a + 13 / 5a + 12 / 5a = 90;
30 / 5a = 90;
a = 90: 6 = 15 cm.

c = 13/5 * 15 = 13 * 3 = 39 cm.

b = 12/5 * 15 = 12 * 3 = 36 cm.

Answer: the sides of the second triangle are 15 cm; 36 cm vs 39 cm.