In trapezoid ABCD AB = CD, height BH divides the base into two segments, the smaller of which is 5 cm.

In trapezoid ABCD AB = CD, height BH divides the base into two segments, the smaller of which is 5 cm.Find AD if the middle line is 9 cm.

Since, by condition, AB = CD, the trapezoid ABCD is isosceles.

By the property of an isosceles trapezoid, the height drawn from the top of an obtuse angle divides the larger base into two segments, the smaller of which is equal to half the difference between the bases of the trapezoid – AH = (AD – BC) / 2, and the larger one is equal to half the sum of the bases HD = (AD + BC) / 2.

Since (AD + BC) / 2, this is the formula for the midline of the trapezoid, then НD = КМ = 9 cm.

Then the base АD = АН + НD = 5 + 9 = 14 cm.

Answer: The length of the base АD = 14 cm.