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
Let's solve the problem step by step:
1. Let's assume the width of the rectangle as x meters.
2. According to the problem, the length of the rectangle is four meters less than twice its width. So, the length would be (2x - 4) meters.
3. The formula for the area of a rectangle is length multiplied by width. So, the area of the rectangle can be calculated as x * (2x - 4).
4. Given that the area of the rectangle is 96 m^2, we can set up the equation x * (2x - 4) = 96.
5. Expanding the equation, we have 2x^2 - 4x = 96.
6. Rearranging the equation, we get 2x^2 - 4x - 96 = 0.
7. Factoring the equation, we have 2(x^2 - 2x - 48) = 0.
8. Simplifying, we have x^2 - 2x - 48 = 0.
9. Factoring further, we get (x - 8)(x + 6) = 0.
10. Setting each factor equal to zero, we have x - 8 = 0 or x + 6 = 0.
11. Solving each equation, we find x = 8 or x = -6. Since the width cannot be negative, we discard the solution x = -6.
12. Therefore, the width of the rectangle is 8 meters.
13. Substituting the value of x back into the expression for length, we have length = 2x - 4 = 2(8) - 4 = 16 - 4 = 12 meters.
So, the length of the rectangle is 12 meters and the width of the rectangle is 8 meters.
What is the area
The area of the rectangle is given by the formula length multiplied by width.
Using the values we found in the previous steps, the width of the rectangle is 8 meters and the length is 12 meters.
Therefore, the area of the rectangle is calculated as:
Area = length * width
= 12 meters * 8 meters
= 96 square meters.
So, the area of the rectangle is 96 square meters.