The length of a rectangle is four meters less than twice its width.
If the area of the rectangle is 96 m^2, what is the length and the width?
An expression for the length of the rectangle in terms of the width would be
Response area
The formula for the area of a rectangle is
Response area
Using trial and error, if the area is 96 m^2, then the length and width are
Response area
Area = 1/2(l x w). l = 4 - 2w. l = 12 & w = 8. l = 8 w = 12. Area = 2l + 2w. L = 2w - 4. W = 2l - 4. L = 24 & w = 4. Area = l x w. L = 2 & w = 24
An expression for the length of the rectangle in terms of the width would be l = 2w - 4.
The formula for the area of a rectangle is Area = length x width.
Using trial and error, if the area is 96 m^2, then one possible set of length and width is:
- Length = 12 meters
- Width = 8 meters
Another possible set of length and width is:
- Length = 8 meters
- Width = 12 meters
However, if we use the given expression for the length in terms of the width (l = 2w - 4), we can solve for the exact values:
- Substitute the expression for l into the formula for the area: (2w - 4)(w) = 96
- Expand and rearrange: 2w^2 - 4w = 96
- Subtract 96 from both sides: 2w^2 - 4w - 96 = 0
- Divide both sides by 2: w^2 - 2w - 48 = 0
- Factorize: (w - 8)(w + 6) = 0
- Set each factor equal to zero and solve for w: w - 8 = 0 or w + 6 = 0
- Solve for w: w = 8 or w = -6
Since width cannot be negative, we discard the width of -6 and conclude that the width is 8 meters.
Plugging this value back into the expression for the length, we can calculate the length: l = 2(8) - 4 = 16 - 4 = 12 meters.
So, the length of the rectangle is 12 meters and the width is 8 meters.