Asked by Sharon
Eighty metres of fencing are available to enclose a rectangular play area. Determine the dimensions that will enclosed the maximum area. What is the maximum area?
Answers
Answered by
Steve
2(x+y)=80, so y = 40-x
area = xy = x(40-x) = 40x-x^2
That's just a parabola. Find the vertex and you will have the maximum area.
A little investigation that the rectangular shape of maximum area for a given perimeter is always a square.
area = xy = x(40-x) = 40x-x^2
That's just a parabola. Find the vertex and you will have the maximum area.
A little investigation that the rectangular shape of maximum area for a given perimeter is always a square.
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