Question

If ∆ABC ~ ∆DEF such that area of ∆ABC is 9 cm² and the area of ∆DEF is 16 cm² and BC = 2.1 cm. Find the length of EF.

Answer 1

Given ∆ABC ~ ∆DEF

∴ `("Area of"  Delta"ABC")/("Area of"  Delta"DEF") = "BC"^2/"EF"^2`  ...(Square of their corresponding sides)

`9/16 = (2.1)^2/"EF"^2`

`(3/4)^2 = (2.1/"EF")^2`

`3/4 = 2.1/"EF"`

EF = `(4 xx 2.1)/3` = 2.8 cm

Length of EF = 2.8 cm