ABCD trapezoid. Diagonal BD is perpendicular to lateral rib BD.

univerkov | February 23, 2021 | education

Since, by condition, the angle АDВ = ВСD, then ВD is the bisector of the angle АDC, and therefore it cuts off the isosceles triangle ВСD. BC = DC.

The ABD triangle is rectangular, and the angle ADB = 30, then the angle BAD = 180 – 90 – 30 = 00.

Then the angle ABD = CDA = 60, which means that the trapezoid is isosceles, AB = CD.

In triangle ABD, leg AB lies opposite angle 30, then hypotenuse AD = 2 * AB.

Let AB = X cm, then AB = BC = CD = X cm, and AD = 2 * X cm.

Then Ravsd = X + X + X + 2 * X = 5 * X = 60 cm.

X = 60/5 = 12 cm, then AD = 2 * 12 = 24 cm.

Answer: The length of the AD base is 24 cm.

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