Question

help please !!!!

Find the dimensions of the rectangular corral
producing the greatest enclosed area given 200 feet of
fencing.

Answer 1

ok so its like-

ur given that-
x+y=200
y=200-x
and the area should be maximum
area=x*y
area=x*(200-x)
area=200x-x^2

u can get the value of x for which the area will be max by differentiating the area equation which we got with respect to x and equating it to 0

so u get

\[\frac{ d}{ dx }(200x-x^2) =0\]
after differentiating u get-
200-2x=0
200=2x
x=100

and we know that y=200-x
so y=200-100
y=100


so the dimensions are x=100 and y=100

so basically if u are maximizing the area then the figure has to become a square even tho we are given that its a rectangle :)