Question

If trangle ABc simillar trangle DEF BC =3cm EF=4cm and ar(trangle ABC) =54cmsquare determin ar (trangleDEF),​

Answer 1

$\underline{\underline{\huge\mathfrak{your\:answer}}}$

ar(∆DEF) = 96 cm^2

step-by-step explanation:

Given,

∆ ABC ~ ∆ DEF

BC = 3 cm

EF = 4 cm

ar(∆ABC) = 54 cm^2

Now,

we have to find ar(∆DEF)

We know that,

by properties of smililar triangles,

if ∆ABC ~ ∆DEF,

then,

ar(∆ABC)/ar (∆DEF) = ${BC}^{2}$/${EF}^{2}$

=> 54/ar(∆DEF) = ${3}^{2}$/${4}^{2}$

=> 54/ar(∆DEF) = 9/16

=> ar(∆DEF) = 54×16/9

=> ar(∆DEF) = 96 cm^2

SO, the ar(∆DEF) is 96 cm^2.