In trapezoid ABCD, diagonal BD is perpendicular to the lateral side AB, angle ADC

| May 7, 2021 | education

In trapezoid ABCD, diagonal BD is perpendicular to the lateral side AB, angle ADC = angle BDC = 30. Perimeter of the trapezoid = 60 Find: AD.

Since the diagonal BD is perpendicular to AB, the triangle ABD is rectangular, in which the angle ADB = 30.

Then the length of the hypotenuse AD = AB * 2 cm.

The diagonal BD is the bisector of the angle ADC, since it divides it in half, then the triangle BCD is isosceles, BC = CD, and the angle CBD = BDC = 30.

Then the angle ABC = 90 + 30 = 120, and therefore the angle BAD = (180 – 120) = 60.

Angle BAD = ADB = 60, then the trapezoid is isosceles, and therefore AB = BC = CD, and AD = 2 * AB.

Then Ravsd = 3 * AB + 2 * AB = 5 * AB.

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

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



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