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

Let's assume the length of a side of an equilateral triangle is 'a' cm.

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

a = perimeter of an equilateral triangle - 120

a = 3a - 120

3a - a = 120

2a = 120

a = 60 cm

Area of the equilateral triangle = $$\frac{\sqrt{3}}{4}\times a^2$$

= $$\frac{\sqrt{3}}{4}\times60^2$$

= $$\frac{\sqrt{3}}{4}\times3600$$

= $$\sqrt{3}\times900$$

= $$900\sqrt{3}$$ $$cm^{2}$$