Find the ratio of the areas of triangles ABC and KMH, if AB = 8 cm, BC = 12 cm, AC = 16 cm

Find the ratio of the areas of triangles ABC and KMH, if AB = 8 cm, BC = 12 cm, AC = 16 cm, KM = 10 cm, MH = 15 cm, HK = 20 cm.

Let us find the ratio of the lengths of the sides of the triangles ABC and KMН.

AB / KM = 8/10 = 4/5.

BC / MH = 12/15 = 4/5.

AC / KН = 16/20 = 4/5.

Since the ratio of the lengths of the similar sides are equal, the ABC triangle is similar to the KMН triangle in three proportional sides.

Then the ratio of the areas of triangles is equal to the square of the coefficient of similarity of triangles.

Sаvs / Sкмн = (4/5) 2 = 16/25.

Answer: The area ratio is 16/25.