Question

if the area of an equilateral triangle is 9 root three
CM sqare​

Answer 1

Answer:

Let the side of the equilateral triangle be x.

For an isoceles triangle or an equilateral triangle, the perpendicular on one side also acts as the median.

So, the height of the perpendicular

= √[x^2 - (x/2)^2]

= √[x^2 - (x^2)/4]

= x(√3)/2

Now the area of the triangle = (1/2) × x × x(√3)/2

= (x^2)(√3)/4

According to the question,

(x^2)(√3)/4 = 9(√3) sq cm

x = 6 cm

So, the perimeter of the equilateral triangle= 3x

= 3 × 6

= 18 cm