Continuation of the lateral sides of the trapezoid ABCD, intersect at point O. find BО and the ratio of the areas

| February 23, 2021 | education

Continuation of the lateral sides of the trapezoid ABCD, intersect at point O. find BО and the ratio of the areas of the triangles BОС and AOD, AD = 5 cm, BC = 2 cm, AO = 25 cm.

Since ABCD is a trapezoid, then AD is parallel to BC, and then the angle OBC = OAD as the corresponding angles at the intersection of parallel straight lines BC and AD secant AO.

In triangles AOD and BOC, the angle at the vertex O is common, then triangles AOD and BOC are similar in two angles.

Then from the similarity of triangles: AD / AO = BC / BO.

ВO = AO * BC / AD = 25 * 2/5 = 10 cm.

Let us determine the coefficient of similarity of triangles AOD and BOС.

K = BC / AD = 2/5.

The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.

Svos / Saod = K ^ 2 = 4/25 ..

Answer: The length of the ВO segment is 10 cm, the area ratio is 4/25.



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