Question

show that the area of an equilateral triangle √3/4 where x is a side of a triangle?

Answer 1

Answer:

Area of equilateral triangle is

$\frac{ \sqrt{3} }{4} {x}^{2}$

. where x is the side of the triangle.

Step-by-step explanation:

Let an equilateral triangle with the side of x units,

Now,

Draw a perpendicular height from any of the vertex.

The perpendicular will divide the triangle in two equal parts.

So,

Length of side in each triangle, on which perpendicular will be drawn, will be half of the total length.

Therefore,

base ( when applying Pythagoras Theorem ) = x / 2

By Pythagoras Theorem,

Length of perpendicular = √[ ( side )^2 - ( side / 2 )^2 ]

Length of perpendicular = √x^2 - x^2 / 4

Length perpendicular = √( 4x^2 - x^2 ) / 4

= √3x^2 / 4

= √3 x / 2

Now,

As we have drawn a perpendicular,

Area of right angled triangle = 1 / 2 × x × √3 x / 2

⇒ √3 / 4 x^2

Hence, proved.