Don sides of triangles PQR and ABC PQ = 16cm QR = 28cm and AB = 12cm
| August 9, 2021 | education
Don sides of triangles PQR and ABC PQ = 16cm QR = 28cm and AB = 12cm BC = 15cm AC = 21cm, find the ratio of the areas of these triangles.
Let’s find the ratio of the sides of triangles ABC and PQR.
AB / PR = 15/20 = 3/4.
BC / PQ = 12/16 = 3/4.
AC / RQ = 21/28 = 3/4.
Since the ratio of the lengths of the sides of the triangles are equal, the triangles ABC and PQR are similar in three proportional sides with the coefficient of similarity K = 3/4.
The ratio of the areas of similar triangles is equal to the squared coefficient of their similarity.
Sас / Spqr = K ^ 2 = 9/16.
Answer: The area ratio is 9/16.
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