Find the length of the side and perimeter of an equilateral triangle whose height is cm.

Let ABC be an equilateral triangle,

Let AP be a perpendicular on side BC from A.

To find : Height of triangle = AP

As, ABC is an equilateral triangle we have

AB = BC = CA = 'a'

Also, we know that Perpendicular from a vertex to corresponding side in an equilateral triangle bisects the side

Now, In ΔABP, By Pythagoras theorem

(Hypotenuse)² = (base)² + (Perpendicular)²

⇒ AB² = BP² + AP²

Given,

Height = √3

⇒ a = 2 cm

Also, Perimeter of equilateral triangle = 3a

Where 'a' depicts side of equilateral triangle.

∴ Perimeter = 3(2) = 6 cm