Question

ΔABC ~ ΔDEF such that ar(ΔABC) = 64 cm² and ar(ΔDEF) = 169 cm². If BC = 4 cm, find EF.

Answer 1

We have Δ ABC ~ Δ DEF
If two triangles are similar then the ratio of their areas is equal to the ratio of the squares of their corresponding sides. 

∴ `(area(ΔABC))/(area(ΔDEF))=((BC)/(EF))^2` 

⇒ `64/169=((BC)/(EF))^2` 

⇒` (8/13)^2=(4/(EF))^2`  

⇒ `8/13=4/(EF)`

⇒ EF = 6.5 cm