Question

The length of a median of an equilateral triangle is √3. Length of the side of the triangle is .......,select a proper option (a), (b), (c) or (d) from given options so that the statement becomes correct.
(a) 1
(b) 2√3
(c) 2
(d) 2√2

Answer 1

Hi ,

In an equilateral triangle ,

altitude ( h ) = median = √3

Let the side of triangle = a

( √3/2 ) a = h

a = 2h/√3

a = ( 2 × √3 )/√3

a = 2

Therefore ,

side = a = 2

Option ( c ) is correct.

I hope this helps you.

: )

Answer 2

Method - 1:

Given that length of median of an Equilateral triangle = $\sqrt{3}$

$= > \frac{\sqrt{3}}{2} * a = \sqrt{3}$

$= > \frac{a}{2} = 1$

$= > a = 2$

Therefore, the length of side of the triangle is 2cm. - Option(C)

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Method : 2

Given that length of median of an equilateral triangle = $\sqrt{3}$

Let the length of side of triangle be x.

In Triangle ADB,

= > AB^2 = BD^2 + AD^2

$= > x^2 = (\frac{x}{2})^2 + (\sqrt{3})^2$

$= > x^2 = \frac{x^2}{4} + 3$

$= > x^2 = \frac{x^2 + 12}{4}$

= > 4x^2 = x^2 + 12

= > 3x^2 = 12

= > x^2 = 4

= > x = 2cm.

Therefore, the length of side of the triangle is 2 cm - Option (C)

Hope this helps!