Question
If `x` is he length of a median of an equilateral triangle , then its area is :
Answer: Option D
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Let the side of the triangle be a, Then ,
`a^2 = (a/2)^2 + x^2`
`hArr (3a^2)/(4) = x^2`
`hArr a^2 = (4x^2)/(3)`
`:.` Area = `sqrt(3)/4 a^2 = sqrt(3)/4 xx 4/3 x^2 = x^2/sqrt(3) = (x^2sqrt(3))/(3)`
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