what is an expression for the perimeter of a square,P, as a function of its area, A?

Question

anonymous · Answer

$$P(A)=4\sqrt{A}$$
The square root of the area of a square is one of its sides, 4 of these is the perimeter

anonymous · Answer

so this was a question on an assignment in my high school orientation. problem is i have no idea how to get that...

anonymous · Answer

p(a) = 4 SQRT(A)

anonymous · Answer

or another way to think about it: Picture a square.  Now imagine making a bigger square by imagining four times as many squares.  How much did area go up?  It got 4x bigger (+3 squares).  What about the perimeter of this larger square?  It got 2x bigger (each of the side lengths doubled).  If you make the area 9x bigger now, you'll see the perimeter is 3x bigger.  The purpose of all of this is seeing how A varies with P, and we can see that A~P^2.  We want this in terms of P though, so we take the root of both sides to arrive at sqrt(A)~P.  To find the four, you can just imagine a square with side length 1, making perimeter 4.  What will area be? 1.  This means that for sqrt(1) to equal 4 you must multiply it by 4, something that won't change as the square gets bigger.

anonymous · Answer

i  think i got it thanks.

anonymous · Answer

You went to a highschool much harder than the one I just graduated from if that was a question at the orientation..

anonymous · Answer

yea probably. and this question was supposed to be the easiest one on the worksheet