Question

The perimeter of an equilateral triangle is 60 m. The area is ______.

Options

• `10sqrt(3)` m² 

• `15sqrt(3)` m² 

• `20sqrt(3)` m² 

• `100sqrt(3)` m² 

Answer 1

The perimeter of an equilateral triangle is 60 m. The area is `underlinebb(100sqrt(3)  m^2)`.

Explanation: 

Let each side of an equilateral be x.

Then, perimeter of an equilateral triangle = 60 m

x + x + x = 60

⇒ 3x = 60

⇒ x = `60/3` = 20 m

Area of an equilateral triangle = `sqrt(3)/4` (Side)² 

= `(sqrt(3)/4) xx 20 xx 20`

= `100sqrt(3)` m² 

Thus, the area of triangle is `100sqrt(3)` m².