You have 80 yards of fencing to enclose a rectangular region.find the dimensions of the rectangle that maximize the enclose area.what is the maximize area? I NEED ALL THE STEPS!

Question

raden · Answer

actually, if u want finish it soon
u can suppose the rectangle has to be a square
so, what's the length of side a square when its perimeter = 80, 
obviously, 20 right ?
so, the area = side * side = 20 * 20 = ....

anonymous · Answer

P=80=2x + 2y|dw:1355020865708:dw|

your area formula is A=xy

Since you have your P equation... you can get your x in terms of y by 
$$\frac{ 2x+2y=80 }{ 2 }$$
which thne you get$$x+y=40$$
so then you get $$x=40-y$$

plug in x for your equation in your area so you get...

$$A = (40-y)y$$

Distribute... so you get
$$A = 40y - y^{2}$$

take the derivative of A so that you get.. $$A' = 40 - 2y$$

set A' = 0 and solve...

$$0 = 40-2y$$
$$-40 = -2y$$
$$20 = y$$

plug back in y for your x equation

$$x = 40-y$$
$$x = 40-20$$
$$x = 20$$

raden · Answer

the finally, the pic be a square :p

anonymous · Answer

is this correct?

anonymous · Answer

yeah it is...

anonymous · Answer

thanks^-^

anonymous · Answer

wait so the answer is 400 then right?

anonymous · Answer

yupp