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Question
Ratio of corresponding sides of two similar triangles is 4:7, then find the ratio of their areas = ?
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)
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 = (4/7)^2` ......[From (i)]
`"A"_1/"A"_2 = 16/49`
∴ Ratio of areas of similar triangles = 16 : 49
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