In a rectangular trapezoid ABCD, the smaller diagonal AC makes an angle of 60 degrees with the base

| June 20, 2021 | education

In a rectangular trapezoid ABCD, the smaller diagonal AC makes an angle of 60 degrees with the base. The perimeter of the triangle ACD is 36 cm. Calculate the length of the midline of the trapezoid if AC = AD.

By condition, the diagonal AC is equal to the larger base, then the ACD triangle is isosceles, and so one of the angles is 60, then the ACD triangle is equilateral, AC = CD = AD.

The perimeter of an equilateral triangle is 36 cm, then AC = CD = AD = 36/3 = 12 cm.

Let’s draw the height CH of the triangle ACD, which is also the median of the triangle, and then AH = DH = AD / 2 = 12/2 = 6 cm.

Quadrilateral BCНD rectangle, then BC = AH = 6 cm.

Determine the length of the midline of the trapezoid. KM = (BC + AD) / 2 = (6 + 12) / 2 = 9 cm.

Answer: The length of the middle line of the trapezoid is 9 cm.



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