Find the ratio of the areas of triangles PQR and ABC, if PQ = 16 cm, QR = 20 cm, PQR АB = 12 cm, BC = 15 cm, AC = 21 cm.

univerkov | January 10, 2021 | education

Let us determine the ratio of the lengths of the sides of the triangles ABC and PQR.
AB / PQ = 12/16 = 3/4.
AC / QR = 15/20 = 3/4.
BC / PR = 21/28 = 3/4.
Since the ratio of the sides of the triangles ABC and PQR are equal, the triangles ABC and PQR are similar in three proportional sides with the coefficient of their similarity K = 3/4.
The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.
Saws / Spqr = K2 = 9/16.
Answer: The area ratio is 9/16.

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