Question 199939
A farmer decides to enclose a rectangle garden using one side of the barn as
 a side to the rectangle. What is the maximum area that the farmer can enclose
 with 100 ft of fence? What should the dimensions of the garden be to give this area?

Maximum area that the farmer can enclose with 100 ft of fence__________sq.ft.
:
Let x = the width of the garden
Let L = the length
:
The perimeter equation for 3 sides:
L + 2x = 100
L = (100-2x)
:
The area equation:
A = x * L
Replace L with (100-2x)
A = x(100-2x)
A = -2x^2 + 100x
:
Find the axis of symmetry of this quadratic equation a=-2; b=100
x = {{{(-100)/(2*-2)}}}
x = {{{(-100)/(-4)}}}
x = +25 ft is the width for max area
:
L = 100 - 2(25)
L = 50 ft
:
Max area: 50 * 25 = 1250 sq/ft