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Question
Areas of two similar triangles are in the ratio 144: 49. Find the ratio of their corresponding sides.
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Solution
Let the areas of two similar triangles be A1, A2 and their corresponding sides be S1, S2 respectively.
∴ `"A"_1/"A"_2 = 144/49` ...(i)[Given]
∴ by the theorem of areas of similar triangles,
∴ `"A"_1/"A"_2 = "S"_1^2/"S"_2^2`
∴ `144/49 = "S"_1^2/"S"_2^2` ...[From (i)]
∴ by taking square root of both sides,
∴ `"S"_1/"S"_2 = 12/7`
∴ The ratio of the corresponding sides of the given triangles is 12: 7.
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