In an isosceles trapezoid with a side of 15 cm, a smaller base 16 cm and a height of 9 cm. Find a larger base.

univerkov | January 1, 2021 | education

Consider a right-angled triangle CDH and, by the Pythagorean theorem, determine the length of the leg of the DH.
DH ^ 2 = SD ^ 2 – CH ^ 2 = 15 ^ 2 – 9 ^ 2 = 225 – 81 = 144.
DH = 12 cm.
According to the property of the height of an isosceles trapezoid, the height drawn from the apex of an obtuse angle divides the larger base into two segments, the smaller of which is equal to the half-difference of the bases.
DH = (BP – BC) / 2.
AD = 2 * DH + BC = 2 * 12 + 16 = 40 cm.
Answer: The length of the larger base is 40 cm.

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