# A parallelogram is inscribed in a triangle, the angle of which coincides with the angle of the triangle.

A parallelogram is inscribed in a triangle, the angle of which coincides with the angle of the triangle. The sides of the triangle enclosing this angle are 20 cm and 25 cm, and the parallel sides of the parallelogram are 6: 5. Determine the sides of the parallelogram.

Let the length of the smaller side of the parallelogram be 5 * X cm, then the pancake of the larger side is 6 * X cm.

Since the AK side of the parallelogram lies on the AC side, and the parallelogram sides are parallel, DE is parallel to AC.

The length of the segment BD = AB – AD = 20 – 5 * X.

Triangles ABC and BDE are similar in two angles.

Then AB / BD = AC / DE.

20 / (20 – 6 * X) = 25/5 * X.

100 * X = 500 – 150 * X.

250 * X = 500.

X = 500/250 = 2.

DE = AK = 5 * 2 = 10 cm.

AD = KE = 6 * 2 = 12 cm.

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

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