To find out the length and width of the rectangle, we need to solve the problem step-by-step.
1. Let's assume the width of the rectangle is "w" meters.
- So, the length of the rectangle would be 2w - 4 meters (four meters less than twice the width).
2. The formula for the area of a rectangle is:
- Area = length × width
3. We know that the area of the rectangle is 96 square meters.
- So, using the formula for the area, we can set up the equation:
96 = (2w - 4) × w
4. Simplifying the equation:
96 = 2w^2 - 4w
5. Rearranging the equation to solve for w:
2w^2 - 4w - 96 = 0
6. Factoring the equation:
(2w + 12)(w - 8) = 0
7. Setting each factor equal to zero and solving for w:
(2w + 12) = 0 or (w - 8) = 0
8. Solving for w:
- (2w + 12) = 0 ---> 2w = -12 ---> w = -6 (reject the negative value)
- (w - 8) = 0 ---> w = 8
9. Now that we have the width, we can find the length:
- Length = 2w - 4 ---> Length = 2(8) - 4 ---> Length = 16 - 4 ---> Length = 12 meters
Therefore, the length of the rectangle is 12 meters and the width is 8 meters.
An expression for the length of the rectangle in terms of the width would be:
- Length = 2w - 4
The formula for the area of a rectangle is:
- Area = length × width
Using trial and error, we found that the length and width are 12 meters and 8 meters, respectively.