Question

The area of an equilateral triangle is given by the formula A=√3/4(s)^2. Which formula represents the length of an equilateral triangle's side (s) in terms of the triangle's area (A)?

Answer 1

$\frac{\sqrt{3}}{4} s^2$ = A

We need to essentially switch s with A

s²√3 = 4A

s² = (4A)/√3

s = √[(4A)/√3]

s = $\sqrt{\frac{4A}{\sqrt{3}}}$

Answer 2

Your answer would be

$s \: = \sqrt{ \frac{4a}{ \sqrt{3} } }$

You can find this by rearranging the formula

$a \: = \frac{ \sqrt{3} }{4} {s}^{2}$

to make s the subject of the formula.

First we can see that this can be written as

$\frac{ {s}^{2} \sqrt{3} }{4}$

Which means we can multiply a by 4 to get:

$4a = {s}^{2} \sqrt{3}$

Then we can divide by √3 :

$\frac{4a}{\sqrt{3} } = {s}^{2}$

And finally square root the whole fraction:

$\sqrt{ \frac{4a}{ \sqrt{3} } } = s$

So this formula represents the side of an equilateral triangle, with 'a' being the area.

I hope this helps!