Question

If $a$ is the side of an equilateral triangle, then its area is given by $\frac{\sqrt{3}}{4}{a}^2$. Given that the area of an equilateral triangle is $5\sqrt{3}$ units, find its side correct to 4 decimal ploaces

Answer 1

We have the equation $\frac{\sqrt{3}}{4}{a}^2=5\sqrt{3}$

Hence
$a^2=\frac{5\sqrt{3}\times 4}{\sqrt{3}}=20$

We find $\sqrt{20}$ up to 5 decimal places and round it off to 4 decimal places as shown in the image.

Thus, $\sqrt{20}=4.47213$

When this is rounded off to 4 decimal places, we get $4.4721$