SOLUTION: Bob has 40 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (20 – x) feet wide. What value of x will give th

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Bob has 40 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (20 – x) feet wide. What value of x will give th      Log On


   

Question 861321: Bob has 40 feet of fencing to enclose a rectangular garden. If one side of the garden is x feet long, he wants the other side to be (20 – x) feet wide. What value of x will give the largest area, in square feet, for the garden?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The dimensions are x, and 20-x.
The fencing to be used will be the perimeter of the garden.
2(x)+2(20-x)=40, and no treatment of area was done yet.
2x+40-2x=40
40=40
This makes like the value of x would not matter - but x value MUST matter.

Area is x(20-x), A%28x%29=20x-x%5E2.
The maximum area will happen in the exact middle of x%2820-x%29=0, because A(x) is a parabola with a maximum point. The x-intercepts are 0 and 20. The middle of them is x=10. This obviously makes the garden a square shape, 10 feet by 10 feet. This will also give the perimeter, 10+10+10+10=40, which is the same as the amount of fencing material to be used.