In an isosceles triangle, the base is half the lateral side, and the perimeter is 37.5 cm. Find the sides of the triangle.

Let’s call the triangle ABC, where AB, BC are the sides, AC is the base. We determine that the length of the base is x cm, then the lengths of the sides are equal to 2x cm, we write down what the perimeter will be:
P = AB + BC + AC = 37.5 cm;
P = 2x + 2x + x = 5x = 37.5 cm;
x = 7.5 cm.
We got that the length of the base is 7.5 cm, then the lengths of the sides AB and BC will be equal:
2x = 2 * 7.5 = 15 cm.
Answer: the length of the sides (AB = BC) is 15 cm, and the length of the base is 7.5 cm.