Question

∆ABC ∼ ∆DEF. If BC = 3 cm, EF = 4 cm and ar(∆ABC) = 54 cm², then ar(∆DEF) =

पर्याय

•  108 cm²

• 96 cm²

• 48 cm²

• 100 cm²

Answer 1

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`