In the trapezoid ABCD AB = CD, BH-height, divides the base into 2 segments

| March 5, 2021 | education

In the trapezoid ABCD AB = CD, BH-height, divides the base into 2 segments, less than AH = 5, find AD if the middle line of the trapezoid is 9cm.

The first way.

The height of an isosceles trapezium, drawn from the top of the smaller base, divides the larger base into two segments, the larger of which is equal to the midline of the trapezoid.

НD = KM = 9 cm.

Then АD = АН + НD = 5 + 9 = 14 cm.

Second way.

Let’s draw another height CH1, then, since the trapezoid is isosceles, the heights are cut off on a larger base equal segments AH = DH1 = 5 cm.

Let the lengths of the segments BC and НН1 be equal to X cm.

Then the middle line of the trapezoid is: KM = 9 = (X + AH + X + H1D) / 2 = (2 * X + 10) / 2.

9 = X + 5.

X = 9 – 5 = 4 cm, then AD = 5 + 4 + 5 = 14 cm.

Answer: AD= 14 cm.



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