Question

∆ABC and ∆DEA are equilateral triangle. If AB 4,
and A (∆ABC) : A (∆DEF) 1:3. then find DE.
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Answer 1

Answer:

4√3

Step-by-step explanation:

Given,

ΔABC and ΔDEF are equilateral

All sides of an equilateral triangle are equal

ie, in ΔABC, AB = BC = CA

AB = 4 units = BC = CA

A (ΔABC) = √3/4 a²

               = √3/4 4²

               = 8√3

A (ΔABC) : A (ΔDEF) = 1:3

1/3 = 8√3/x

x = 24√3

DE = √3/4 a² = 24√3

     = 4√3

∴DE = 4√3