Question

find the area of an equilateral triangle whose perimeter is 180 cm​

Answer 1

All the sides of an equilateral triangle is equal

let the side be a

Perimeter = 180cm

=> 3a = 180

=> a = 180/3

=> a = 60cm

Area of an equilateral triangle = √3 a²/4

=> √3 × (60)²/4

=> √3 × 3600/4

=> √3 × 900

=> 900√3 cm²

Answer 2

${\huge {\underline {\tt {\blue {Answer}}}}}$

Let the sides be x

= x + x + x = 180

= 3x = 180

= x = 180/3

= x = 60

The side of the triangle is 60,

Area of equilateral triangle ,

= $\displaystyle\frac {\sqrt{3}}{4}×{side}^{2}$

= $\displaystyle\frac {\sqrt{3}}{4}×{60}^{2}$

= $\displaystyle\frac {\sqrt{3}}{4}×3600$

= $\sqrt{3} × 900$

= 1.73 × 900

= 1558.84 cm Square.

_________________________