Given a triangle ABC, in which AB = 6 cm, AC = 10 cm. On its sides points are taken: M belongs to AB

| September 5, 2021 | education

Given a triangle ABC, in which AB = 6 cm, AC = 10 cm. On its sides points are taken: M belongs to AB, N belongs to BC, K belongs to AC. It is known that AMNK is a rhombus. Find the perimeter of the diamond.

Since AMNK is a rhombus, AM = MH = NK = AK.

Let the length of the side of the rhombus be X cm, then H = X cm, BM = (6 – X) cm.

In a rhombus, opposite sides are parallel, MH is parallel to AK.

Then the triangles ABC and BMH are similar in two angles, the angle B of the triangles is common, the angle BAC = BMH as the corresponding angles at the intersection of parallel lines AC and ML secant AB.

From the similarity of triangles:

MH / AC = BM / AB.

X / 10 = (6 – X) / 6.

6 * X = 60 – 10 * X.

16 * X = 60.

X = 60/16 = 3.75 cm.

Then Ravsd = 4 * 3.75 = 15 cm.

Answer: The perimeter of the rhombus is 15 cm.



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