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Question
The ratio of corresponding sides of similar triangles is 3 : 5; then find the ratio of their areas.
Solution
Let the ratio of corresponding sides of similar triangles be S1 and S2 and A1 and A2 be their corresponding areas.
Given: The two triangles are similar.
S1 : S2 = 3 : 5
∴ `("S"_1)/("S"_2) = 3/5` ...(i)
By Theorem of areas of similar triangles,
`("A"_1)/("A"_2) = ("S"_1)^2/("S"_2)^2`
`("A"_1)/("A"_2) = (("S"_1)/("S"_2))^2`
`("A"_1)/("A"_2) = (3/5)^2` ...[From (i)]
`("A"_1)/("A"_2) = 9/25`
∴ The ratio of areas of similar triangles = 9 : 25.
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