# What will be the Each Side of the Triangle ? If

On decreasing each side of an equilateral triangle by 2 cm, there is a decrease of 4√3 cm square in its area. The length of each side of the triangle is

- 6cm
- 8cm
- 3cm
- 5cm

**Answer: (4) 5 cm**

**Explanation:-**

Let be the side of a equilateral triangle = a cm

Then, the area of a equilateral triangle = √3a^{2}/4

Side is decreased by 2 cm

Then, the side = (a – 2) cm

The new area of triangle = √3(a- 2)^{2}/4

According to the question,

√3a^{2}/4 – √3(a- 2)^{2}/4 = 4√3

a^{2} – (a – 2)^{2} = 4 x 4

a^{2} – a^{2} – 4 + 4a = 16

4a = 16 + 4 = 20

a = 20/4

a = 5

Hence, the answer is (4) 5 cm.