The middle line of the trapezoid ABCD splits it into two trapeziums, the middle lines of which
| September 24, 2021 | education
The middle line of the trapezoid ABCD splits it into two trapeziums, the middle lines of which are 15 cm and 19 cm, find the base of the trapezoid ABCD.
Consider a trapezoid PELK, whose base lengths are 15 cm and 19 cm, then its middle line is MH = (EL + PK) / 2 = (15 + 19) / 2 = 34/2 = 17 cm.
Consider a trapezoid АМНD, for which the middle line and a smaller base are known, then we define its larger base.
RK = (MH + AD) / 2.
19 = (17 + AD) / 2.
AD = 19 * 2 – 17 = 38 – 17 = 21 cm.
Consider a trapezoid MBCH, for which the middle line and a larger base are known, then we define its smaller base.
EL = (BC + MH) / 2.
15 = (BC + 17) / 2.
BC = 15 * 2 – 17 = 30 – 17 = 13 cm.
Answer: The bases of the trapezoid ABCD are 13 and 21 cm.
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