Question

If the area of an equilateral triangle is `25 sqrt(3)  cm^2`, find its perimeter.

Answer 1

Given: Area of equilateral triangle = `25sqrt(3)  cm^2`.

Step-wise calculation:

1. Formula for area of an equilateral triangle with side length a: 

`Area = sqrt(3)/4 a^2`

2. Substitute the given area:

`25sqrt(3) = sqrt(3)/4 a^2`

3. Divide both sides by `sqrt(3)`: 

`25 = 1/4 a^2`

4. Multiply both sides by 4: 

100 = a²

5. Take square root: 

a = 10 cm

6. Perimeter of an equilateral triangle is: 

Perimeter = 3a

Perimeter = 3 × 10

Perimeter = 30 cm

The perimeter of the equilateral triangle is 30 cm.