The height of the trapezoid is 7 cm and one of the bases is 5 times smaller than the other

The height of the trapezoid is 7 cm and one of the bases is 5 times smaller than the other, find the bases of the trapezoid if its area is 84 cm2.

In order to calculate the area of the trapezoid ABCD, it is necessary to divide the sum of the lengths of its bases BC and AD by two and multiply by the length of the height BH:

S = (a + b) / 2 h.

Since one of its bases is five times less than the other, we express it as follows:

x is the length of the smaller base of the BC;

5x – the length of the larger AD base;

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

6x / 2 7 = 84;

3x 7 = 84;

3x = 84/7;

3x = 12;

x = 12/3 = 4;

BC = 4 cm;

AD = 5 4 = 20 cm.

Answer: the smaller base BC is 4 cm, the larger base is 20 cm.