Question

Δ ABC ~ Δ DEF. If BC = 3cm , EF=4cm and area of  Δ ABC = 54 cm² ,  find area of  Δ DEF.

Answer 1

Given : Δ ABC  ∼    Δ DEF

To find : Ar. of Δ DEF

Sol : `("Ar." triangle  "ABC")/("Ar." triangle  "DEF") = "BC"^2/"EF"^2`    

[The ratio of areas of two triangles is equal to the ratio of square of their corresponding sides.]

`54 / ("Ar" triangle "DEF") = (3/4)^2`

`54 / ("Ar" triangle "DEF") = (9/16)`

Ar Δ DEF = `(54 xx 16)/9`

= 96 cm²