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In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio 4 : 9, find the ratio of the areas of ∆ABC and ∆PQR - Mathematics

Sum

In two similar triangles ABC and PQR, if their corresponding altitudes AD and PS are in the ratio 4 : 9, find the ratio of the areas of ∆ABC and ∆PQR

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Solution

Since the areas of two similar triangles are in the ratio of the squares of the corresponding altitudes.

`\therefore \text{ }\frac{Area\ (\Delta ABC)}{Area\ (\DeltaPQR)}=(AD^2)/(PS^2)`

`=>(Area(DeltaABC))/(Area(DeltaPQR)) =(4/9)^2=16/81` [∵AD:PS=4:9]

Hence, Area (∆ABC) : Area (∆PQR) = 16 : 81

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