The radius of a circle inscribed in a rectangular trapezoid is 8 cm, the middle line of this trapezoid is 18 cm

| February 15, 2021 | education

The radius of a circle inscribed in a rectangular trapezoid is 8 cm, the middle line of this trapezoid is 18 cm, find the side of the trapezoid.

Knowing the length of the midline of the trapezoid, we determine the sum of the lengths of its bases.

MR = 18 = (BC + AD) / 2.

(BC + AD) = 18 * 2 = 36 cm.

Since a circle is inscribed in the AВСD trapezoid, then by the property of a quadrangle into which a circle can be inscribed, the sum of the lengths of its opposite sides are equal.

BC + AD = AB + СD = 36 cm

The diameter of the inscribed circle is equal to the length of the height of the trapezoid, and since the trapezoid is rectangular, its lateral side is AB. AB = D = 2 * R = 2 * 8 = 16 cm.

AB + СD = 36 cm.

СD = 36 – AB = 36 – 16 = 20 cm.

Answer: The sides of the trapezoid are 16 cm and 20 cm.



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