Question

Angle ABC and Angle DEF are equterial triangles If [Angle ABC] A

Answer 1

Step-by-step explanation:

Answer:

Length of the side DE is 4√2.

Step-by-step explanation:

Given: Δ ABC and Δ DEF are Equilateral triangles.

ar(Δ ABC) : ar(Δ DEF) = 1 : 2

AB = 4

To find length of DE.

We know that All Equilateral triangles are similar to each other.

So, we use a result which states that,

If two triangles are similar then ratio of the area of triangles is equal to square to the ratio of the corresponding sides.

So we have,

\frac{\Delta\,ABC}{\Delta\,DEF}=(\frac{AB}{DE})^2

ΔDEF

ΔABC

=(

DE

AB

)

2

\frac{1}{2}=(\frac{4}{DE})^2

2

1

=(

DE

4

)

2

\sqrt{\frac{1}{2}}=\frac{4}{DE}

2

1

=

DE

4

\frac{1}{\sqrt{2}}=\frac{4}{DE}

2

1

=

DE

4

DE=4\sqrt{2}DE=4

2

Therefore, Length of the side DE is 4√2.