SOLUTION: A farmer plans to use 220 feet of fencing and a side of her barn to enclose a rectangular garden​. What dimensions of the rectangle would give the maximum​ area? What i
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Question 1082491: A farmer plans to use 220 feet of fencing and a side of her barn to enclose a rectangular garden. What dimensions of the rectangle would give the maximum area? What is that area?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Let = the length of a side that
is perpendicular to the barn
The sides will be:
, , and
----------------------------------
The area of the rectangular garden is:
The plot of this is a parabola. It has the form:
( )
The formula for the x-coordinate of the
vertex ( maximum in this case ) is:
---------------------------
Plug this result back into equation.
The maximum area is 6050 ft2
----------------------------------
check:
The sides are:
so:
and
The total length of fence is:
OK
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