The midline of a trapezoid is 2/3 of the larger base, how many times is the midline of a trapezoid larger than its smaller base?

We denote by x the length of the larger base of this trapezoid, and by y – the length of the smaller base of this trapezoid.

According to the condition of the problem, the length of the midline of this trapezoid is 2/3 of the length of the larger base of this trapezoid.

Since the length of the midline in any trapezoid is equal to half the sum of the lengths of the bases of this trapezoid, we can make the following ratios:

(2/3) x = (x + y) / 2.

From this ratio we get:

2 * 2x = 3 * (x + y);

4x = 3x + 3y;

4x – 3x = 3y;

x = 3y.

Find the ratio of the length of the midline to the length of the smaller base:

((x + y) / 2) / y = ((3y + y) / 2) / y = (4y / 2) / y = 2y / y = 2.

Answer: The middle line is 2 times the length of the smaller base.