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.
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