The bases of the isosceles trapezoid. The bases of the isosceles trapezoid are 33 and 75

| June 20, 2021 | education

The bases of the isosceles trapezoid. The bases of the isosceles trapezoid are 33 and 75, the lateral side is 75. Find the length of the diagonal of the trapezoid.

Let’s draw from the top of an obtuse angle B the height BH to the base of AD.

According to the property of height, an isosceles trapezoid drawn from the apex of an obtuse angle, the height divides the larger base into two segments, the smaller of which is equal to the half difference of the bases, and the larger half the sum of the bases.

AH = (AD – BC) / 2 = (75 – 33) / 2 = 21 cm.

DH = (AD + BC) / 2 = (75 + 33) / 2 = 108/2 = 54 cm.

From the right-angled triangle AHB, according to the Pythagorean theorem, we determine the length of the leg BH.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 75 ^ 2 – 21 ^ 2 = 5625 – 441 = 5184.

BH = √5184 = 72 cm.

From the right-angled triangle ВНD we determine the length of the diagonal ВD.

BD ^ 2 = BH ^ 2 + DH ^ 2 = 72 ^ 2 + 54 ^ 2 = 5184 + 2916 = 8100.

ВD = √8100 = 90 cm.

Answer: The length of the diagonal of the trapezoid is 90 cm.



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