The bases of the trapezoid are 7 cm and 15 cm. Find the segment of the diagonal into which the second diagonal divides

| April 26, 2021 | education

The bases of the trapezoid are 7 cm and 15 cm. Find the segment of the diagonal into which the second diagonal divides it, if the difference between these segments of the pavna is 24 cm.

Let the length of the segment OC = X cm, then, by condition, OA = 24 + X cm.

Let us prove that triangle BOC is similar to triangle AOD.

Angle BOC = AOD as vertical angles at the intersection of diagonals AC and BD.

Angle OCB = ОАD as criss-crossing angles at the intersection of parallel BC and AD secant AC. Then the triangles BOC and AOD are similar in two angles.

From the similarity of triangles: BC / AD = OC / OA.

7/15 = X / (24 + X).

15 * X = 168 + 7 * X.

8 * X = 168.

X = OC = 168/8 = 21 cm.

OA = 24 + 21 = 45 cm.

Answer: The diagonal is divided into 21 cm and 45 cm segments.



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