Question

Find the perimeter of an equilateral triangle whose area is `36sqrt(3)  "cm"^2`.

Answer 1

Given: Area = `36sqrt(3)  "cm"^2`; let side = a cm.

Step-wise calculation:

1. Area formula for an equilateral triangle: A = `(sqrt(3)/4) a^2`.

2. Substitute: `(sqrt(3)/4) a^2 = 36sqrt(3)`

3. Divide both sides by `sqrt(3) : a^2/4 = 36`

4. Multiply by 4: a² = 144

5. Take positive root: a = 12 cm

6. Perimeter P = 3a 

= 3 × 12

= 36 cm