The diagonals of the trapezoid ABCD intersect at the point O, AD // BC, AO / OC = 5/2, and the middle line

| May 28, 2021 | education

The diagonals of the trapezoid ABCD intersect at the point O, AD // BC, AO / OC = 5/2, and the middle line of the trapezoid is 7 cm. Find the base of the trapezoid.

Let the length of the segment OS = 2 * X cm, then the length of the segment OA = 5 * X cm.

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

Then BC / AD = OC / OA = 2 * X / 5 * X = 2/5.

2 * AD = 5 * BC.

BC = 2 * AD / 5.

The middle line of the trapezoid is: KM = (BC + AD) / 2 = 2 * AD / 5 + AD) / 2 = 7.

7 * AD / 5 = 2 * 7.

AD = 2 * 5 = 10 cm.

BC = 2 * 10/5 = 4 cm.

Answer: The lengths of the bases are 4 cm and 10 cm.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.