One side of the triangle is 2.5 times smaller than the second and 16 cm less than the third.

One side of the triangle is 2.5 times smaller than the second and 16 cm less than the third. Find the sides of the triangle if its perimeter is 52 cm.

Let’s write the first side of the triangle as x cm.

Since this side is 2.5 times smaller than the second, the length of the second will be: 2.5 * x.

The length of the third side will be: x + 16 cm.

Since the perimeter of a triangle is the sum of all its sides, we get the equation:

x + 2.5 * x + x + 16 = 52.

4.5 * x = 52 – 16.

4.5 * x = 52 – 16.

4.5 * x = 36.

x = 36 / 4.5 = 8 cm (first side).

2.5 * x = 2.5 * 8 = 20 cm (second side).

x + 16 = 8 + 16 = 24 cm (third side).

Answer: The sides are 8, 20 and 24 cm.