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

Find the ratio of the areas of triangles ABC and KMN if AB = 8 cm BC = 12cm AC = 16cm KM = 10cm MN = 15cm NK = 20cm

1. We calculate the ratios of the sides of the given triangles ABC and KMN:

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

BC: MN = 12:15 = 4/5.

AC: NK = 16:20 = 4/5.

2. Based on the results of the above calculations, we conclude: the given triangles are similar, since their sides are proportional. And 4/5 is the coefficient of similarity (k).

3. According to the properties of such triangles, the ratio of their areas is equal to k².

k² = 16/25.

Answer: The ratio of the area of the triangle KMN to the area of the triangle ABC is 16/25.