What is the largest area that can be fenced off of a rectangular garden if it will be fenced off with 220 feet of available material?

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Answer 1 · 2015-02-25T22:39:43

It will be a square garden.

Let's do the maths:

Let's call the dimensions of the garden #x# and #y#
Then we can immediately get rid of #y# because the circumference of the fence is #220ft#, so:

#2x+2y=220->2y=220-2x->y=110-x#

Now we come to area #A# (substituting #y#)

#A=x*y=x(110-x)=110x-x^2#

To find the maximum we set the derivative to #0#

#A'=110-2x=0->x=55->y=110-55=55#
(see earlier equation)

Answer : Area #A=55*55=3025 ft^2#