The diagonals divide the middle line of the trapezoid into three parts, the length of which

univerkov | September 17, 2021 | education

The diagonals divide the middle line of the trapezoid into three parts, the length of which is 7cm, 8cm, 7cm. Find the main trapezoid.

Consider a triangle ABC.

Since, by condition, МН is the middle line of a trapezoid, then AM = BM and МН parallel to BC, then MK is parallel to BC, and therefore MK is the middle line of triangle ABC, which is equal to half of BC.

MK = BC / 2.

BC = 2 * MK = 2 * 7 = 14 cm.

Let us determine the length of the middle line of the MH.

MN = MK + KR + PH = 7 + 8 + 7 = 22 cm.

From the formula for the midline of the trapezoid, we determine the length of the base AD.

MH = (AD + BC) / 2.

AD = 2 * MН – BC = 2 * 22 – 14 = 30 cm.

Answer The bases of the trapezoid are 14 m and 22 cm.

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