The height is equal to the trapezoid, drawn from the top with a smaller base, divides the larger base

univerkov | April 30, 2021 | education

The height is equal to the trapezoid, drawn from the top with a smaller base, divides the larger base into segments of length 11 and 17. Find the length of the smaller base.

Determine the length of the base AD.

AD = AH + DH = 11 + 17 = 28 cm.

Since, by condition, the trapezoid ABCD is isosceles, its height, drawn from the top of the obtuse angle, divides the larger base into two segments, the smaller of which is equal to the transparency of the bases AH = (AD – BC) / 2, and the greater, half the sum of the bases DH = (AD + BC) / 2.

Then (AD – BC) / 2 = 11 cm.

(28 – BC) = 11 * 2.

BC = 28 – 22 = 6 cm.

Answer: The length of the smaller base is 6 cm.

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