Question 360405
A rectangular garden, 21m^2 in area, will be fenced 
 Find the dimensions that will require the least amount of fencing if a barn
 already protects one side of the garden.
:
Let x = the width 
Let L = the length
:
since the barn is one side the perimeter:
p = L + 2x
:
The given area:
L * x = 21
L = {{{21/x}}}
:
Replace L in the perimeter equation with {{{21/x}}}
p = {{{21/x}}} + 2x
:
Graph this on a graphing calc, find the minimum (p = the y axis)
{{{ graph( 300, 200, -4, 10, -10, 50, (21/x) + 2x) }}}
min: x = 3.24 meters is the width
L = {{{21/3.24}}}
L = 6.48 meters is the width
:
Sumarize, a garden of 6.48 by 3.24 meter gives 21 sq/m using minimum fencing.
(About 13 meters of fencing)
:
:
Check this, find the area with these dimensions
6.48 * 3.24 = 20.99 ~ 21