In trapezoid ABCD, diagonal BD is perpendicular to the lateral side AB, angles ADB and BDC

| June 3, 2021 | education

In trapezoid ABCD, diagonal BD is perpendicular to the lateral side AB, angles ADB and BDC are 30 degrees, find the length AD if the perimeter of the trapezoid is 60 cm.

According to the condition, the angle ADB = BDC = 30, then the angle DBC = BDA as criss-crossing angles at the intersection of parallel lines AD and BC secant BD, then the triangle BCD is isosceles, BC = CD.

Consider a right-angled triangle ABD, which, by condition, has angle B = 90, angle D = 30, then angle A = 180 – 90 – 30 = 60.

The leg AB of the triangle ABC lies opposite the angle 30, then the hypotenuse AD = 2 * AB.

Since the angle BAD = CDA = 60, the trapezoid ABCD is isosceles, AB = BC.

AB = BC = CD, and AD = 2 * AB.

Let AB = X cm, then Ravsd = X + X + X + 2 * X = 60 cm.

5 * X = 60.

X = 12 cm.

AD = 2 * X = 2 * 12 = 24 cm.

Answer: AD = 24 cm.



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