I have 180 meters of string, I need to make a maximum area rectangle shape out of it. How the formula for area should sound like?

Question

vocaloid · Answer

perimeter = 2L + 2W

with me so far?

anonymous · Answer

Yes

phi · Answer

Is this calculus ?

vocaloid · Answer

then if

180 = 2W + 2L 

then 

90 = W + L, with me so far?

anonymous · Answer

Yes, then area= x(x-90) right?

vocaloid · Answer

almost

vocaloid · Answer

90 = W + L 

means that

W = 90 - L

so area = (90-L)*L

(or x in your case)

anonymous · Answer

so  then S(x)=-x^2 +90x, and the maximum I get is 90 which for me doesn't make sense

phi · Answer

you should take the derivative of your function, and set it equal to zero

or, if you notice  
y= -x^2+90x
has the shape of a parabola, you are finding the peak (i.e. vertex of this $\cap$ shape)
where the slope is 0