In a rectangular trapezoid, the diagonal drawn from the top of the obtuse angle is equal to the side.

univerkov | June 29, 2021 | education

In a rectangular trapezoid, the diagonal drawn from the top of the obtuse angle is equal to the side. Find the ratio of the larger base of the trapezoid to the midline.

Since, by condition, AC = DC, the ACD triangle is isosceles. Let’s draw the height of CH, which in triangle ACD will also be the median of the triangle, then AH = DH.

Quadrilateral ABCH is a rectangle, since BC and CH are perpendicular to the bases of the trapezoid, then BC = AH = AH = AD / 2.

Determine the length of the midline of the trapezoid.

KM = (BC + AD) / 2 = (AD / 2 + AD) / 2 = 3 * AD / 4.

Then AD / KM = AD / (3 * AD / 4) = 4/3.

Answer: The ratio of the larger base to the midline is 4/3.

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