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Question
Ratio of corresponding sides of two similar triangles is 4 : 7, then find the ratio of their areas = ?
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Solution
Let the corresponding sides of similar triangles be s1 and s2.
Let A1 and A2 be their corresponding areas.
s1 : s2 = 4 : 7 ...[Given]
∴ `(s_1)/(s_2) = 4/7` ...(i)
`(A_1)/(A_2) = (s_1^2)/(s_2^2)` ...[Theorem of areas of similar triangles]
`(A_1)/(A_2) = (s_1/s_2)^2`
`(A_1)/(A_2) = (4/7)^2` ...[From (i)]
`(A_1)/(A_2) = 16/49`
∴ Ratio of areas of similar triangles = 16 : 49
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