The length of a side of an equilateral triangle is 120 cm less than its perimeter. What is the area of the equilateral triangle?

$900 \sqrt{3}$ cm²

We know that,

Area of a equilateral triangle = \(\frac{\sqrt {3}}{4}\) × (side)²

We have,

The length of a side of an equilateral triangle = 120 cm less than its perimeter. 

According to the question,

3(side) - 120 = (side)

= 2(side) = 120

= (side) = 60

Area of the triangle = \(\frac{\sqrt {3}}{4}\) × (60)² = \(\frac{\sqrt {3}}{4}\) × 3600

= 900\(\sqrt {3}\) cm²