A circle is inscribed in the trapezoid, the perimeter of which is 56 cm.

univerkov | September 7, 2021 | education

A circle is inscribed in the trapezoid, the perimeter of which is 56 cm. The three consecutive sides of the trapezoid are in the ratio 2: 7: 12. Find the sides of the trapezoid.

Since a circle is inscribed in the trapezoid, the sum of the sides of the trapezoid is equal to the sum of the lengths of its bases.

(BC + AD) = (AB + CD).

Let the side length BC = 2 * X cm, then, by condition, CD = 7 * X cm, AD = 12 * X cm.

Then (AB + 7 * X) = (2 * X + 12 * X).

AB = 14 * X – 7 * X = 7 * X.

By condition, the perimeter of the trapezoid is 56 cm, then.

14 * X + 14 * X = 56.

X = 56/28 = 2.

AB = CD = 2 * 7 = 14 cm.

BC = 2 * 2 = 4 cm.

AD = 2 * 12 = 24 cm.

Answer: The sides of the trapezoid are 14 cm, 4 cm, 14 cm, 24 cm.

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