The side and base of an isosceles triangle are proportional to the numbers 5 and 2.

The side and base of an isosceles triangle are proportional to the numbers 5 and 2. Find the sides of the triangle if its perimeter is 36 cm.

Let the lengths of the sides of the triangle be 5 * X and 2 * X.

The sides BC and AB cannot have a length of 2 * X, since the condition for constructing a triangle is not met, 2 * X + 2 * X is less than 5 * X.

Then AC = 2 * X, AB = BC = 5 * X.

Ravs = 36 = 2 * X + 5 * X + 5 * X = 12 * X.

X = 36/12 = 3.

AB = BC = 3 * 5 = 15 cm, AC = 2 * 3 = 6 cm.

Answer: The lengths of the sides of the triangle are 6 cm, 15 cm, 15 cm.