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Question
∆ABC ∼ ∆DEF. If BC = 3 cm, EF = 4 cm and ar(∆ABC) = 54 cm2, then ar(∆DEF) =
Options
108 cm2
96 cm2
48 cm2
100 cm2
Solution
Given: In Δ ABC and Δ DEF
`Δ ABC ∼ Δ DEF`
`Ar (ΔABC)=54 cm^2 `
`BC=3cm`and `EF=4cm`
To find: Ar(Δ DEF)
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
`(Ar(ΔABC))/(Ar(ΔDEF))=(BC)^2/(EF)^2`
`(54)/(Ar(ΔDEF))=3^2/4^2`
`(54)/(Ar(ΔDEF))=9/6`
`(54)/(Ar(ΔDEF))= (16xx54)/9`
`Ar(ΔDEF)=96 cm^2`
Hence the correct answer is `b`
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