Question

ΔABC and ΔDEF are equilateral triangles. If A(ΔABC):A(ΔDEF)=1:2 and AB=4, find DE.

Answer 1

Final Answer: $\boxed{DE=4 \sqrt{2} \:\:units }$ 

 Steps:
1) We know, 
Two Equilateral triangles are always similar. 

So, Ratio of area of two similar triangles is equal to ratio of square of corresponding sides. 

$\frac{ar(ABC)}{ar(DE)F}= \frac{ AB^{2} }{ DE^{2} } \\ \\ =\ \textgreater \ \frac{1}{2} = \frac{ 4^{2} }{ DE^{2} } \\ \\ =\ \textgreater \ DE= 4 \sqrt{2} units$ 

Hence,DE=4 root(2) units .