In the trapezoid, the upper base is 6cm, and the lower base is 1.5 times the midline. find the average length.

The middle line of a trapezoid is equal to the half-sum of the bases of this trapezium and is parallel to them:

m = (BC + AD) / 2.

Since the length of the smaller base is known to us, it is equal to 6 cm, and the length of the larger base is one and a half times the length of the midline, we express it this way:

x is the length of the midline m;

1.5x – the length of the lower base AD;

(6 + 1.5x) / 2 = x;

6 + 1.5x = 2x;

6 = 2x – 1.5x;

6 = 0.5x;

x = 6 / 0.5 = 12.

In this way:

m = 12 cm;

AD = 1.5 12 = 18 cm.

Answer: The middle line of the trapezoid is 12 cm.