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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
Solution
∆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
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