Question

A ∆(ABC) and A∆(DEF)=1:2 if AB=4 then what is length of DE?
A) 2√√2 2)4 c)8 D)4√2​

Answer 1

Answer:

Ans - 4√2

Step-by-step explanation:

Given ∆ABC and ∆DEF are equilateral triangle

∆ABC : ∆DEF = 1:2

AB = 4

TO FIND DE :-

We know that all equilateral triangles are similar to each other

So, we use a result that states

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

So we have,

∆ABC

---------- = ( AB. )²

∆DEF ( ---------- )

( DE. )

½ =. ( 4)²

(---------)

( DE)

√½ = 4

----

DE

DE = 4√ 2