ABCD-convex quadrilateral angle B = angle A = 90 degrees, AB = 6, BC = 8, DC = 3X. Find: АD.

univerkov | May 5, 2021 | education

Since the angle A and B are equal to 90, the quadrilateral ABCD is a rectangular trapezoid.

Let’s build the height of the CH. Quadrangle ABCH is a rectangle, then CH = AB = 6 cm, AH = BC = 8 cm.

In a right-angled triangle CDH, according to the Pythagorean theorem, DH ^ 2 = CD ^ 2 – AH ^ 2 = 9 * X ^ 2 – 36.

DН = 3 * √ (X ^ 2 – 4) cm.

Then AD = AH + DH = 8 + 3 * √ (X ^ 2 – 4) see.

Answer: The length of the AD side is 8 + 3 * √ (X ^ 2 – 4) cm.

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