One of the legs of a right-angled triangle is 15 cm, and the second leg is 5 cm less than

One of the legs of a right-angled triangle is 15 cm, and the second leg is 5 cm less than the hypotenuse. Find the perimeter of the triangle.

1. Vertices of triangle A, B, C. Leg BC = 15 cm. AB – hypotenuse.

2. The length of the AC leg is taken as x (cm), (x + 5) cm – the length of the hypotenuse AB.

3. Let’s make the equation:

15² + x² = (x + 5) ²;

225 + x² = x² + 10x + 25;

10x = 200;

x = 20 cm – length of the AC leg.

AB = 20 + 5 = 25 cm.

4. Calculate the total length of all sides of the triangle (perimeter):

25 + 15 + 20 = 60 cm.

Answer: the total length of the sides of a given triangle (perimeter) is 60 cm.