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Question
Areas of two similar triangles are 225 cm2 and 81 cm2. If side of smaller triangle is 12 cm, find corresponding side of major triangle.
Solution
Let the areas of two similar triangles be A1 and A2.
A1 = 225 cm2 and A2 = 81 cm2
Let the corresponding sides of triangles be s1 and s2 respectively.
s1 = 12 cm
`"A"_1/"A"_2 = "s"_1^2/"s"_2^2` ...[Theorem of areas of similar triangles]
∴ `225/81 = "s"_1^2/12^2`
∴ s12 = `(225 xx 12^2)/81`
∴ s1 = `(15 xx 12)/9` ...[Taking square root of both sides]
∴ s1 = 20 cm
∴ The length of the corresponding side of the bigger triangle is 20 cm.
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