Question

A rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals. What dimensions should be used so that the enclosed area will be a maximum?

Answer 1

maximation problem
your given the fencing of 200 (perimeter)
2length + 2width = 200
and you want to maximize area
length(width) = area

solve for length
length = 100 - width
substitute into area
(100-width)(width) = 100width - width^2
take derivative
with respect to width and set = to 0

100 - 2width = 0
solve for width
100 = 2width
width = 50
plug and solve for length
length = 100 -50 = 50

Answer 2

lol sorry i didnt see that pic let me try again

Answer 3

your perimeter = 4x + 2y = 200
area = xy

solve for x
4x=200-2y
x = 50 - y/2
subsitute into area

area = (50-y/2)(y)
= 50y - y^2/2
take derivative and set = 0

50 - y = 0
y = 50
plug and solve for x

x = 50 - 50/2
x = 25