Write an equation that represents the area.
Solve for all values of x.
What is the length and width of the rectangle?
A rectangle has an area of 40 square units. The length is represented by x-2 and the width is represented by x+4.
To find the area of a rectangle, we use the formula A = length x width.
Given that the area is 40 square units, the equation that represents the area is: (x-2)(x+4) = 40
Expanding the equation:
x^2 + 4x - 2x - 8 = 40
x^2 + 2x - 8 = 40
x^2 + 2x - 48 = 0
Now, we can solve for x by factoring or using the quadratic formula. Factoring the equation, we get:
(x+8)(x-6) = 0
Therefore, x = -8, 6
Since the length is represented by x-2 and the width is represented by x+4, we can substitute the values of x into the expressions to find the length and width of the rectangle.
For x = -8:
Length = -8 - 2 = -10
Width = -8 + 4 = -4
For x = 6:
Length = 6 - 2 = 4
Width = 6 + 4 = 10
Therefore, the length and width of the rectangle are 10 units by 4 units.
Are you sure?
Let's recheck the calculations:
Given that the area is 40 square units, the equation that represents the area is: (x-2)(x+4) = 40
Expanding the equation:
x^2 + 4x - 2x - 8 = 40
x^2 + 2x - 8 = 40
x^2 + 2x - 48 = 0
Now, we can solve for x by factoring or using the quadratic formula. Factoring the equation, we get:
(x+8)(x-6) = 0
Therefore, x = -8, 6
Let's plug the values of x in the expressions to find the length and width of the rectangle.
For x = -8:
Length = -8 - 2 = -10
Width = -8 + 4 = -4
For x = 6:
Length = 6 - 2 = 4
Width = 6 + 4 = 10
The length and width of a rectangle cannot be negative, so x = 6 is the valid solution.
Therefore, the length and width of the rectangle are 4 units by 10 units. Thank you for pointing out the error.