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Question
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
Solution
The ratio of the areas of two similar triangles is equal to the ratio of the squares of the corresponding sides.
∴ `("area"(Δ"ABC"))/("area"(Δ"PQR")) = "AB"^2/"DE"^2`
⇒ `(169)/(121) = (26^2)/"DE"^2`
⇒ DE2 = `(121 xx 676)/(169)`
⇒ DE2 = 484
⇒ DE = 22cm.
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