The perimeters of two similar triangles are 20 cm and 30 cm then the ratio of the areas of the triangles is ………
The perimeters of two similar triangles are 20 cm and 30 cm then the ratio of the areas of the triangles is ………
(A) 2 : 3
(B) 3 : 2
(C) 4 : 9
(D) 9 : 4
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Correct option is (C) 4 : 9
Given perimeters of similar triangles are 20 cm and 30 cm.
\(\therefore\) Ratio of perimeters of similar triangles is \(\frac{20}{30}\)
\(=\frac23=2:3\)
\(\therefore\) Ratio of corresponding sides of similar triangles = 2:3
\((\because\) Ratio of corresponding sides of similar triangles = Ratio of perimeters of similar triangles)
\(\therefore\) Ratio of areas of similar triangles \(=(\frac23)^2\)
\(=\frac49=4:9\)
\((\because\) Ratio of areas of similar triangle = (Ratio of corresponding sides of similar triangles\()^2)\)
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