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

| February 1, 2021 | education

In trapezoid ABCD, the diagonal BD is perpendicular to the side AB, angle ABD = angle BDC = 30 degrees. Find: length AD if the perimeter is 60cm.

In the ABC triangle, according to the condition, the angle ADВ = 30, and the angle AВD = 90, then the angle ВAD = 180 – 90 – 30 = 60.

Since ВD is the bisector of the ВDС angle, then the ВAD angle = ВDС + СDВ = 30 + 30 = 60, therefore, the trapezoid is isosceles and AB = СD.

The AB leg lies opposite an angle of 30, which means it is equal to half of the hypotenuse of blood pressure.

AD = 2 * AB.

Let the length AB = X cm, then AD = 2 * AB.

In the ВСD triangle, according to the condition, the ВСD angle = 30, and the DCB angle = ВDA as a cross at the intersection of parallel ABP and ВС secant ВD, then the ВСD angle = СВD, and the ВСD triangle is isosceles, and ВС = СD = AB = X cm.

Then the perimeter of the trapezoid is:

P = AB + BC + СD + AD = X + X + X + 2 * X = 5 * X = 60 cm.

X = 60/5 = 12 cm.

AB = BC = СD = 12 cm.

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

Answer: Length of blood pressure = 24 cm.



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