as with all these problems, the maximum area is attained when the fencing is divided equally between lengths and widths. In this case, since there are no missing sides or internal divisions, that means a square.
So, with 1000m of fencing, the maximum area is when the pen is a square 250m on a side.
maximum area is 250^2 m^2
1000m of fencing is to be used to make a rectangular enclosure,Find the greatest possible area,and the corresponding dimensions if the length of the enclosure is xm and the width is (500-x)m.
3 answers
250
let the lenght of the rectangle be x meters.
Then, the witdh is (1000-2x)/2 meters. So the width will be 500-x meters.
The area A of the rectangle is x*(500-x) da/dx of 500x-x^2 is 500-2x which is equal to 0.
Make x the subject and get x = 250.
Area is maximum when x=250 m.
Area=250*(500-250) which is equal to 62500m^2.
Then, the witdh is (1000-2x)/2 meters. So the width will be 500-x meters.
The area A of the rectangle is x*(500-x) da/dx of 500x-x^2 is 500-2x which is equal to 0.
Make x the subject and get x = 250.
Area is maximum when x=250 m.
Area=250*(500-250) which is equal to 62500m^2.
2 answers