The perimeter of an isosceles triangle is 56 cm. Find the length of the base of this triangle if the side to base ratio is 2: 3.

Let ABC be an isosceles triangle. AB and BC are the sides. AC is the base of the triangle. Its perimeter is P (ABC) = 56. The side to base ratio is 2: 3.
2 * x – the length of the sides AB and BC.
3 * x – base length AC.
Perimeter P (ABC) = AB + BC + AC. From here we can find x:
56 = 2 * x + 2 * x = 3 * x;
56 = 7 * x;
56/7 = 7 * x / 7;
x = 8.
Then the lengths of the sides AB and BC are equal to x * 2 = 8 * 2 = 16, and the length of the base AC = x * 3 = 8 * 3 = 24.