A farmer is fencing a field with an area of 220 m2. He wants the length of the field to be 9 m longer than the width. What should he use for the dimensions of the field?
Let's assume the width of the field is x meters. According to the given information, the length of the field would be x + 9 meters since it is 9 meters longer than the width.
The formula for the area of a rectangle is A = length * width.
In this case, the area of the field is 220 m², so we can write the equation as:
220 = (x + 9) * x
Expanding the equation:
220 = x² + 9x
Rearranging the equation to have it equal to zero:
x² + 9x - 220 = 0
Now, we need to solve this quadratic equation. Factoring it or using the quadratic formula will give us:
(x - 10) (x + 22) = 0
This equation has two possible solutions:
x - 10 = 0 --> x = 10
or
x + 22 = 0 --> x = -22
Since measurements cannot be negative, we can disregard the second solution.
Therefore, the width of the field is 10 meters and the length is x + 9 = 10 + 9 = 19 meters.
Thus, the dimensions of the field should be 10 meters by 19 meters.