In trapezoid ABCD, the diagonal BD is perpendicular to the side AB, angle ABD = angle BDC = 30.

| January 13, 2021 | education

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

Consider the ВСD triangle. The angle of the internal combustion engine is equal to the angle of ADВ as the intersecting angles at the intersection of parallel straight lines BC and AD secant aircraft. Since, by condition, the ADВ angle is equal to the ВDС angle, then the ВDС angle = DBC = 300, then the ВСD triangle is isosceles and ВС = СD.
Consider a triangle AED, which, by condition, has an angle B of a straight line, and an angle D = 30, then the angle DAВ = 180 – 90 – 30 = 60. Since the angle DAВ = 60, and the angle ADС = 30 + 30 = 60, then the trapezium is isosceles and AB = SD.
In the AED triangle, the leg AB lies opposite the angle 30, therefore, it is equal to half of the hypotenuse of blood pressure, then blood pressure = AB * 2.
Let AB = X cm, then AB = BC = СD = X cm, AD = 2 * X.
The perimeter of the trapezoid is: P = AB + BC + СD + AD = X + X + X + 2 * X = 5 * X = 60.
X = 60/5 = 12 cm.
AD = 2 * 12 = 24 cm.
Answer: AD = 12 cm.



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