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

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

Given: triangles ABC and KMN,
AB = 8 cm,
BC = 12cm,
AC = 16 cm,
KM = 10 cm,
MN = 15 cm,
NK = 20 cm.
Find: the ratio of the areas of triangles ABC, KMN -?
Solution: Consider triangles ABC and KMN. Find the ratio: AB / KM = 8 cm / 10 cm = 4/5, BC / MN = 12 cm / 15 cm = 4/5, AC / NK = 16 cm / 20 cm = 4/5. Consequently, the ABC and KMN rectangles are similar in the third feature of similarity (in three proportional sides). The ratio of the areas of similar triangles is equal to the coefficient of similarity squared. Then Sаvs / Sкмn = (4/5) squared = 16/25.
Answer: 16/25.