In the trapezoid ABCD BD is perpendicular to the lateral side AB, the angle ADC is equal to the angles BDC is 30

| September 17, 2021 | education

In the trapezoid ABCD BD is perpendicular to the lateral side AB, the angle ADC is equal to the angles BDC is 30 ° find the length AD if the perimeter of the trapezoid is 60 °

Consider the angles BDA and DBC, which are equal as criss-crossing angles at the intersection of parallel straight lines AD and BC of the secant BD. ∠DBC = ∠BDC = 30.

In the BCD triangle, the angles at the base of BD are equal, therefore the triangle is isosceles and BC = CD.

Determine the value of the angle BAD. ∠BAD = 180 – ∠ABD – ∠DBC = 180 – 90 – 30 = 60.

At the base of the trapezoid, the angles at the base of AD are equal, therefore, the trapezoid is equilateral and AB = CD.

In a right-angled triangle ABD, leg AB lies opposite angle 30, hence AD ​​= 2 * AB.

The perimeter of the trapezoid is P = 60 = AB + BC + CD + AD = AB + AB + AB + 2 * AB = 6 * AB.

AB = 60/6 = 10 cm.

Then AD = 2 * AB = 2 * 10 = 20 cm.

Answer: AD = 20 cm.



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