Write an equation that represents the area.

Question

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.

Answer 1

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.

Answer 2

Are you sure?

Answer 3

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.