if x is the length of a median an equilateral triangle..., Area, General Mathematics

Question:If x is the length of a median of an equilateral triangle, then its area is :

A `x^2` 
B `1/2 x^2` 
C `(x^2sqrt(3))/2` 
D `(x^2sqrt(3))/3`

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+ AnswerD

+ ExplanationLet the side of the triangle be a.

`a^2 = (a/2)^2 + x^2 or (3a^2)/4`

  `x^2 or 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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