A rectangular playground is to be fenced off and divided

garnentas3m 2021-12-18 Answered
A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Four hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?
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Expert Answer

Janet Young
Answered 2021-12-19 Author has 32 answers
The five, fenced sides add up to 400. Subtract 2x from both sides
2x+3y=4003y=4002x
Divide 3 from both sides
y=400323x
Area of a rectangle (in terms of x)
Area=xy=x(400323x)=23x2+4003x=f(x)
x=b2a
x-coordinate of vertex =40032(23)=100
Plug in 100 for x into the y equation.
y-coordinate of vertex =400323(100)=66.6
Plug in 100 for x and 66.6 for y into the area equation.
Area=xy=100(66.6)=6666.6

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