SOLUTION: 3. A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden. a) Write an expression for the perimeter of th

Question 1143074: 3. A man wishes to have a rectangular shaped garden in his backyard. He has 84 feet of fencing with which to enclose his garden.
a) Write an expression for the perimeter of the garden.
b) The area of the garden is A = l*w. Use the perimeter equation from part (a) to write the area in terms of just one variable.
c) Find the dimensions for the largest area garden he can have if he uses all the fencing.
Found 2 solutions by ikleyn, josmiceli:
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.

See the lesson
    - A rectangle with a given perimeter which has the maximal area is a square
in this site.

Find the solution of this problem there and learn it once and for all.

Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
a)
Let = width
Let = length
Let = perimeter
--------------------------------

--------------------------------
b)

--------------------------------
c)

The maximum area is at:

where:

and

For maximum area,

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