SOLUTION: A rectangular garden, 21m^2 in area, will be fenced to keep out rabbits and skunks. Find the dimensions that will require the least amount of fencing if a barn already protects one

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Question 360405: A rectangular garden, 21m^2 in area, will be fenced to keep out rabbits and skunks. Find the dimensions that will require the least amount of fencing if a barn already protects one side of the garden.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Fx
:
Replace L in the perimeter equation with 21%2Fx
p = 21%2Fx + 2x
:
Graph this on a graphing calc, find the minimum (p = the y axis)
+graph%28+300%2C+200%2C+-4%2C+10%2C+-10%2C+50%2C+%2821%2Fx%29+%2B+2x%29+
min: x = 3.24 meters is the width
L = 21%2F3.24
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