8th Grade Math
1. The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 square meters, what is the length and the width?
An expression for the length of the rectangle in terms of the width would be __________________.
The formula for the area of a rectangle is ___________.
Using trail and error, if the area is 96m^2, then the length and width are ___________.
An expression for the length of the rectangle in terms of the width would be 2w - 4.
The formula for the area of a rectangle is length times width (A = l * w).
Using trial and error, if the area is 96m^2, then the length and width are 12m and 8m respectively.
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.