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MCQ

If the length of a median of an equilateral triangle is *x* cm, then its area is

#### Options

x

^{2}- \[\frac{\sqrt{3}}{2} x^2\]
- \[\frac{x^2}{\sqrt{3}}\]
- \[\frac{x^2}{2}\]

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#### Solution

We are given the length of median of an equilateral triangle by which we can calculate its side. We are asked to find area of triangle in terms of *x*

Altitude of an equilateral triangle say *L,* having equal sides of *a *cm* *is given by, where, *L = x *cm

`x = sqrt(3)/2 a`

`a = 2/sqrt(3) x cm `

Area of an equilateral triangle, say *A*_{1} having each side *a* cm is given by

`A_1 = sqrt(3)/4 a^2`

Since `a = 2/sqrt(3) x cm `.So

`A_1 = sqrt (3)/4 (2/sqrt(3) x )^2`

`A_1 = sqrt(3)/4 xx (4x^2)/3`

`A_1 = x^2/sqrt(3)`

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals

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