Question

Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm² and 121 cm². If EF = 15.4 cm, find BC

Answer 1

It is given that ΔABC ~ ΔDEF

`:. (ar(triangleABC))/(ar(triangleDEF)) = ((AB)/(DE))^2 = ((BC)/(EF))^2=((AC)/(DF))^2`

Given that

EF = 15.4

ar(ΔABC) = 64 cm²

ar(ΔDEF) = 121 cm²

`:.(ar(ABC))/(ar(ΔDEF))=((BC)/(EF))^2`

`=>((64 cm^2)/(121 cm^2)) = (BC^2)/(15.4 cm)^2`

`=>(BC)/15.4 = (8/11)cm`

`=>BC = ((8xx15.4)/11)cm = (8 xx 1.4) cm = 11.2 cm`