The height of the trapezoid is 7cm, and one of the bases is 5 times larger than the other.

The height of the trapezoid is 7cm, and one of the bases is 5 times larger than the other. Find the bases of a trapezoid if its area is 84.

Let’s denote by the unknown variable x centimeters – the smaller base of the trapezoid,

Then 5x centimeters is the larger base of the trapezoid.

The area of the trapezoid is equal to the half-sum of the bases multiplied by the height of the trapezoid:

84 = (x + 5x) / 2 * 7;

84 = 21x;

x = 4 centimeters – the smaller base of the trapezoid,

5 * 4 = 20 centimeters – larger base of the trapezoid.

Answer: the bases of the trapezoid are 4 and 20 centimeters.