The point of intersection of the diagonals of the trapezoid divides one of them in the ratio 7:15, and the sum of the bases

univerkov | April 26, 2021 | education

The point of intersection of the diagonals of the trapezoid divides one of them in the ratio 7:15, and the sum of the bases of the trapezoid is 88 cm. Find the bases of the trapezoid.

Triangles BOC and AOD are similar in two angles, since the angle BOC = AOD as vertical angles, the angle OBC = ODA as criss-crossing angles at the intersection of parallel straight lines BC and AD of the secant BD.

Determine the coefficient of similarity of the triangle.

K = ВO / OD = 7/15.

Then BC / AD = 7/15.

7 * AD = 15 * BC.

AD = 15 * BC / 7.

By condition, BC + AD = 88.

BC + 15 * BC / 7 = 88.

22 * BC = 7 * 88.

BC = 7 * 4 = 28 cm.

Then AD = 88 – 28 = 60 cm.

Answer: The lengths of the bases of the trapezoid are 28 cm and 60 cm.

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