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Maharashtra State BoardSSC (English Medium) 10th Standard

Areas of two similar triangles are in the ratio 144 : 49. Find the ratio of their corresponding sides.

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Question

Areas of two similar triangles are in the ratio 144 : 49. Find the ratio of their corresponding sides.

Sum
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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]

∴ `(A_1)/(A_2) = (S_1^2)/(S_2^2)`   ...[Theorem of areas of similar triangles]

∴ `144/49 = (S_1^2)/(S_2^2)`    ...[From (i)]

∴ `(S_1)/(S_2) = 12/7`   ...[Taking square root of both sides]

∴ The ratio of the corresponding sides of the given triangles is 12 : 7.

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Chapter 1: Similarity - Exercise

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