Question

If the length of each side of an equilateral triangle is increased by 2 unit, the area is found to be increased by $3 + \sqrt{3}$ square unit. The length of each side of the triangle is

• A. $$\sqrt{3}units$$
• B. 3 units
• C. $$3\sqrt{3}units$$
• D. $$1+3\sqrt{3}units$$

Answer 1

Answer:

$$\sqrt{3}units$$

Side of equilateral triangle $= x units.$

$\frac{\sqrt{3}}{4}((x+2)^2-x^2)=3+\sqrt{3}$

$\frac{\sqrt{3}}{4}(4x+4)=3+\sqrt{3}$

=>\sqrt{3}x+\sqrt{3}=3+\sqrt{3}

=>\sqrt{3}x=3

=>x=\frac{3}{\sqrt{3}}

$x= \sqrt{3}units$