Question

∆ABC and ∆DEF are equilateral triangles, A(∆ABC): A(∆DEF) = 1: 2. If AB = 4 then what is length of DE? 

Options

• 2√2

• 4 

• 8 

• 4√2

Answer 1

∆ABC and ∆DEF are equilateral triangles.    ...(Given)

In ∆ABC and ∆DEF,
`{:(∠"B" ≅ ∠"E"),(∠"A" ≅ ∠"D"):}          ...("Measure of equilateral triangles is 60°")`
∴ ∆ABC ~ ∆DEF       ...(By AA test of similarity)

By the Theorem of areas of similar triangles,

∴ `("A"(∆"ABC"))/("A"(∆"DEF")) ="AB"^2/"DE"^2`

∴ `1/2 = 4^2/"DE"^2`

Taking square root both sides,

∴ `1/sqrt2 = 4/"DE"`

∴ DE = 4√2 units