Question

If each side of an equilateral triangle be increased by 2 cm, its area is increased by 2$\sqrt{3}$ sq. cm. The length of each side of the original triangle is

• A. 1 cm
• B. $\sqrt{3}$
• C. 3 cm
• D. $\sqrt{3}$ + 2 cm

Answer 1

Answer: (A)

1 cm

Let original side be $a.$

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

According to the question,

$\Rightarrow$ $\frac{\sqrt{3}}{4}\times (a+2{)}^2=\frac{\sqrt{3}}{4}{a}^2+2\sqrt{3}$

$\Rightarrow$ $\sqrt{3}[\frac{1}{4}\times (a^2+4a+4\left)\right]=\sqrt{3}(\frac{1}{4}{a}^2+2)$

$\Rightarrow$ $\frac{a^2}{4}+a+1=\frac{a^2}{4}+2$

$\Rightarrow$ $\frac{a^2}{4}-\frac{a^2}{4}+a=2-1$

$\therefore$ $a=1cm$