A farmer is fencing a field with an area of 220 m^2. 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 represented by "w" meters.
According to the given conditions, the length of the field can be represented as "w + 9" meters.
The formula for the area of a rectangle is given by A = length × width.
We are given that the area of the field is 220 m². So, we can set up the equation:
220 = (w + 9) × w
Expanding the equation, we get:
220 = w² + 9w
Rearranging the equation and setting it equal to zero, we have:
w² + 9w - 220 = 0
Factoring the quadratic equation, we get:
(w + 20)(w - 11) = 0
So, we have two possible solutions for w: w = -20 and w = 11.
Since the width of the field cannot be negative, we discard the solution w = -20.
Therefore, the width of the field is 11 meters.
Using this value, we can find the length:
Length = Width + 9 = 11 + 9 = 20 meters
So, the farmer should use the dimensions 11 meters for the width and 20 meters for the length.