Question

A rectangle has a length of (x+7) and a width of (x-4). Select all the equations that describe the area, A, of the rectangle in terms of x.

A) A = (x + 7)(x - 4)
B) A = 2(x + 7)(x - 4)
C) A = x^2 + 3x - 28
D) A = 2x^2 - x - 28

Answer 1

The correct equations describing the area of the rectangle are A = (x + 7)(x - 4) and A = x² + 3x - 28, which correspond to options A and C.

Step-by-step explanation:

To find the equations that describe the area of a rectangle with length (x+7) and width (x-4), we start by recalling the formula for the area of a rectangle, which is length times width. Applying this formula to the given dimensions of the rectangle, we get the area A as:

A = (x + 7)(x - 4)

Expanding this equation gives us:

A = x² + 7x - 4x - 28

A = x² + 3x - 28

Comparing the given options:

• Option A, A = (x + 7)(x - 4), is the correct initial expression for the area.
• Option B, A = 2(x + 7)(x - 4), incorrectly doubles the area.
• Option C, A = x² + 3x - 28, is the correct expanded expression for the area.
• Option D, A = 2x² - x - 28, does not correspond to the area of the given rectangle.

Therefore, the correct equations that describe the area of the rectangle in terms of x are provided in options A and C.