A parallelogram is inscribed in a triangle, in which all the vertices are located on the sides of the triangle

| September 18, 2021 | education

A parallelogram is inscribed in a triangle, in which all the vertices are located on the sides of the triangle and the angle coincides with the angle of the triangle. The sides of the trackgolnik adjacent to this angle are equal to 20cm and 25cm, and the parallel sides of the parallelogram are referred to as 5: 6 find the sides of the parallelogram.

Since the opposite sides of the parallelogram are parallel, the MP is parallel to the AC.

Let the length of the side MP = AH = 5 * X cm, then the length of the side PH = AM = 6 * X cm.

Triangles ABC and MBP are similar in two angles. Angle B in triangles is common, angle BMP = BAC as the corresponding angles at the intersection of parallel straight lines МР and АС secant AB.

The length of the segment BM = AB – AM = (20 – 6 * X).

Then AB / BM = AC / MР.

20 / (20 – 6 * X) = 25/5 * X.

100 * X = 500 – 150 * X.

250 * X = 500.

X = 500/250 = 2.

Then PH = AM = 2 * 6 = 12 cm.

AH = MR = 2 * 5 = 10 cm.

Answer: The sides of the parallelogram are 10 cm and 12 cm.



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