Sum

Let Δ ABC ~ Δ DEF and their areas be, respectively, 64 cm^{2} and 121 cm^{2}. If EF = 15.4 cm, find BC

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#### Solution

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 cm^{2}

ar(ΔDEF) = 121 cm^{2}

`:.(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`

Concept: Areas of Similar Triangles

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