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