Question

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?

Answer 1

perimeter = 2L + 2W

with me so far?

Answer 2

Yes

Answer 3

Is this calculus ?

Answer 4

then if

180 = 2W + 2L

then

90 = W + L, with me so far?

Answer 5

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

Answer 6

almost

Answer 7

90 = W + L

means that

W = 90 - L

so area = (90-L)*L

(or x in your case)

Answer 8

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

Answer 9

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