The perimeter of an isosceles trapezoid is 60 cm. The larger base is 2 times the size of the smaller base

The perimeter of an isosceles trapezoid is 60 cm. The larger base is 2 times the size of the smaller base. The lateral side is 9 cm larger than the smaller base. Calculate the lengths of the sides of the trapezoid.

Let us denote by x the length of the smaller base of this isosceles trapezoid, expressed in centimeters.

Let us express in terms of x the length of the larger base and the length of the lateral side of this isosceles trapezoid.

According to the condition of the problem, the larger base of this trapezoid is 2 times larger than its smaller base, therefore, the length of the larger base is 2x cm.

It is also known that the lateral side of this isosceles trapezoid is 9 cm larger than its smaller base, therefore, the length of the lateral side is x + 9 cm.

According to the condition of the problem, the perimeter of this trapezoid is 60 cm, therefore, we can draw up the following equation:

x + 2x + 2 * (x + 9) = 60.

We solve the resulting equation:

3x + 2x + 18 = 60;

5x = 60 – 18;

5x = 42;

x = 42/5;

x = 8.4 cm.

Knowing the length of the smaller base, we find the lengths of the larger base and side:

2x = 2 * 8.4 = 16.8 cm,

x + 9 = 8.4 + 9 = 17.4 cm.

Answer: the length of the smaller base is 8.4 cm, the length of the larger base is 16.8 cm, the length of the lateral side is 17.4 cm.