A farmer has 2000 meters of fencing. He wants to enclose a rectangular filed on the side of a river with no fencing along the river. Find the length and the width of the field if the area of the field is 500,000 square meters.

Step-by-step explanation:

If x is the width of the field in the direction perpendicular to the river, then 2000-2x is the length along the river. The total area is ...

  x(2000 -2x) = 500000

  x^2 -1000x +250000 = 0  . . . . . rearrange to standard form

  (x -500)^2 = 0 . . . . . . . . . . . . . . . factor

  x = 500 . . . . one solution

The field is 1000 meters long (along the river) and 500 meters wide.