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?

Answer 1

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.