# The diagonal of a trapezoid divides its midline into two segments so that one of them is 2 times

March 23, 2021 | education

| **The diagonal of a trapezoid divides its midline into two segments so that one of them is 2 times larger than the other. Find the bases of the trapezoid if the midline is 18 cm.**

By condition, the length of MH = 2 * KН.

Let the length of the segment KH = X cm, then MH = 2 * X cm.

KM = KН + MН = X + 2 * X = 18 cm.

3 * X = 18.

X = KH = 18/3 = 6 cm.

MH = 2 * 6 = 12 cm.

Point K is the middle of AB, the segment KН is parallel to BC, then KН is the middle line of triangle ABC, then BC = 2 * KН = 2 * 6 = 12 cm.

Similarly, MH is the middle line of the AСD triangle, then the length of BP = 2 * MH = 2 * 12 = 24 cm.

Answer: The lengths of the bases are 12 cm and 24 cm.