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.
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