Posted by Anonymous on Thursday, November 3, 2011 at 11:02am.
You have 32 feet of fencing and want to determine the maximum area that can be enclosed with the fencing to make a flower garden. You do not want to deal with fractions or decimals, so you are limiting the dimensions to whole numbers. Also, the area is to be rectangular (or square) in shape.

geometry  Reiny, Thursday, November 3, 2011 at 12:37pm
not much of a problem here ...
the largest rectangle is obtained when that rectangle is a square, so
4 equal sides equal 32 feet,
each side is 8 feet
area is 64 square ft

geometry  tchrwill, Friday, November 4, 2011 at 10:52am
Considering all rectangles with a given perimeter, which one encloses the largest area?
The traditional calculus approach would be as follows.
Letting P equal the given perimeter and "x" the short side of the rectangle, we can write for the area A = x(P  2x)/2 = Px/2  x^2.
Taking the first derivitive and setting equal to zero, dA/dx = P/2  2x = 0, x becomes P/4.
With x = P/4, all four sides are equal making the rectangle a square.
.....The short side is P/4.
.....The long side is (P  2(P/4))/2 = P/4.
Therefore, it can be unequivicaly stated that of all possible rectangles with a given perimeter, the square encloses the maximum area.
Answer This Question
Related Questions
 Math  A rectangular garden is to be fenced off and divided into 3 equal regions...
 Maath:)  Sam is going to plant a rectangular flower garden next to his house. ...
 Math OPTIMIZATION  A home gardener plans to enclose two rectangular gardens ...
 Algebra and Trig  Aldo has feet of fencing. He will use it to form three sides ...
 precalc  area of a rectangular region: a farmer wishes to create two ...
 algebra 1  Charles wants to build a vegetable garden such that three sides of ...
 Polynomials and quadratic application  I want to make a rectangular garden by ...
 Math  A rectangular garden is surrounded by a roll of chicken wire fencing to ...
 Math  A rancher has 220 feet of fencing to enclose a rectangular corral. Find ...
 Algebra ( QUAdratic)  a person plans to fence a pig pen with 100 meters of ...
More Related Questions