Moneyman,
You first have to know the following formula for the area of an equilateral triangle:
area = s^2 * sqroot3/4, where s is a measure of a side of the triangle.
Since you are told that the side of a triangle is t, you just square the t and get:
t^2sqroot3/4
The formula for the area of a square is easy enough: side squared.
s^2
Now, you are told that the two areas equal to one another.
The tricky part is to follow algebra without pulling a silly mistake:
s^2 = t^2 sqroot3/4 [multiply both sides by 4]
4s^2 = t^2 sqroot3 [divide both sides by s^2]
4 = t^2 sqroot3/s^2 [multiply both sides by 1/sqroot3]
4/sqroot3 = t^2/s^2 [get rid of the squares by sqroot-ing both sides]
sqroot4/sqroot of sqroot3 = t/s
2/sqroot of sqroot3 = t/s [here is where a lot of people make the mistake, they reduce the two sqroots and get 2:3, which is WRONG]
sqroot of 3 is actuall 3 taken to the power of one half [1/2]
the sqroot sign has a 2 that we do not write because it is such a common operation [for example you do write the 3 when you take a cube root of something]
Therefore, when you see a sqroot of a sqroot of 3, it is really:
sqroot3^(1/2) the two in the denominator is then multiplied by the "invisible" 2 in the sqroot sign, yielding a 4.
Hope this helps.
Sorry I didn't help you before, I was being an ass.
