Question

ΔABC and ΔDEF are equilateral triangles, A(ΔABC) : A(ΔDEF) = 1:2 If AB = 4 then what is length of DE? Select the appropriate alternative
(A) 2√2
(B) 4
(C) 8
(D) 4√2

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 .

Answer 2

Step-by-step explanation:

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

DE=4

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.

\begin{gathered}\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}\end{gathered}

ar(DE)F

ar(ABC)

=

DE

2

AB

2

= \textgreater

2

1

=

DE

2

4

2

= \textgreater DE=4

2

units

Hence,DE=4 root(2) units .