Question

AABC and ADEF are equalateral triangles.
A(AABC): A(ADEF)=1:2. If AB = 4 then
what is length of DE?​

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,

$\frac{\Delta\,ABC}{\Delta\,DEF}=(\frac{AB}{DD}}$

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

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

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

$DE=4\sqrt{2}DE=4$

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