The sides of triangles PKM u ABC are given: PK = 16cm KM = 20cm PM = 28cm AB = 12cm

| June 17, 2021 | education

The sides of triangles PKM u ABC are given: PK = 16cm KM = 20cm PM = 28cm AB = 12cmBC = 15cm AC = 21cm. find the area ratio and the ratio of the perimeters of these triangles.

Let us prove that triangles РКМ and АВС are similar.

Let us find the ratio of the lengths of the sides of the triangles РКМ and АВС.

AB / PK = 12/16 = 3/4.

AC / PM = 21/28 = 3/4.

BC / KM = 15/20 = 3/4.

Then the triangle RKM is milked by the triangle ABC along three proportional sides, the third sign of the similarity of triangles, and their similarity coefficient is K = 3/4.

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

Savs / Srkm = K ^ 2 = (3/4) ^ 2 = 9/16.

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

Rvkm / Ravs = K = 3/4.

Answer: The ratio of the areas of the triangles is 9/16, the ratio of the perimeters of the triangles is 3/4.



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