Question

The area of an equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2 decimal places.

Answer 1

Let each side of the equilateral triangle = x

∴ Its area = `sqrt(3)/4 x^2`

Area perimeter = 3x

By the given condition = `sqrt(3)/4 x^2 = 3x`

`x^2 = 3x xx 4/sqrt(3)`

`x^2 = (3x xx 4 xx sqrt(3))/(sqrt(3) xx sqrt(3)) = (3x xx 4 xx sqrt(3))/3 = 4xsqrt(3)`

⇒ `x^2 = sqrt(3) (4x) ⇒ x = 4sqrt(3)`   [∵ x ≠ 0]

∴ Perimeter = `12sqrt(3)` units

= 12 (1.732) = 20.784 = 20.78 units