Question

can anybody answer me this in full details as early as possible​

Answer 1

Let the side of an equilateral triangle be a

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

According to the question

$\frac{ \sqrt{3} }{4} (a + 2)^{2} = \frac{ \sqrt{3} }{4} {a}^{2} + 2 \sqrt{3} \\ (a + 2)^{2} = \frac{ \frac{ \sqrt{3} }{4} {a}^{2} + 2 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } \\(a + 2)^{2} = \frac{ \frac{ \sqrt{3} }{4} {a}^{2} }{ \frac{ \sqrt{3} }{4} } + \frac{2 \sqrt{3} }{ \frac{ \sqrt{3} }{4} } \\ (a + 2) ^{2} = {a }^{2} + 2 \sqrt{3} \times \frac{4}{ \sqrt{3} } \\ {a}^{2} + 4 + 4a = {a}^{2} + 8 \\ 4 + 4a = 8 \\ 4a = 8 + 4 \\ 4a = 12 \\ a = \frac{12}{4} \\ a = 3$

Therefore, side of an equilateral triangle= 3cm