In the trapezoid ABCD, the segment MN connects the midpoints of the lateral sides, and it is equal to the half-sum of the bases

In the trapezoid ABCD, the segment MN connects the midpoints of the lateral sides, and it is equal to the half-sum of the bases. Find the length MN if it is known that it MN is 1.5 times less than the larger base and 4 more less than the base.

Let’s denote the length of the midline through X cm.

MH = X cm.

Then, by condition, BC = (MH – 4) = (X – 4).

AD = MH * 1.5 = X * 1.5.

Then:

MH = (BC + AD) / 2 = ((X – 4) + 1.5 * X) / 2 = X.

X – 4 + 1.5 * X = 2 * X.

2.5 * X – 2 * X = 4.

0.5 * X = 4.

X = MH = 8 cm.

Answer: The length of the middle line of the trapezoid is 8 cm.