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Question
The areas of two similar triangles are 16cm2 and 9cm2 respectively. If the altitude of the smaller triangle is 1.8cm, find the length of the altitude corresponding to the larger triangle.
Solution
The ratio of the areas of two similar triangles is equal to the ratio of the square of the corresponding altitudes.
∴ `("area"(Δ"ABC"))/("area"(Δ"PQR")) = "AL"^2/"DM"^2`
⇒ `(16)/(9) = "AL"^2/1.8^2`
⇒ AL2 = `(16 xx 3.24)/(9)`
⇒ AL2 = 5.76
⇒ AL = 2.4cm.
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