Question

The length of a rectangle is 8 less than 4 times the width. The area of the rectangle is 32 square inches.

Write two equations to model the area of the rectangle, A. Let W represent the width of the rectangle.
Use the keypad to enter the answers in the boxes.
equation 1: A =
equation 2: A =

Answer 1

The first equation is A = W × (4W - 8), representing the area based on the relationship between length and width. The second equation is A = 32, representing the fixed area of the rectangle. These equations are used to solve for the dimensions of the rectangle.

Step-by-step explanation:

The first equation to represent the area (A) of the rectangle in terms of the width (W) stems from the description given:

A = length × width

According to the problem, the length is 8 less than 4 times the width, which we can express as:

Length = 4W - 8

Now we use the formula for the area of a rectangle to get:

Equation 1: A = W × (4W - 8)

Since the area is given as 32 square inches, we can set this equation equal to 32 to get our second equation:

Equation 2: A = 32

Meaning the area of the rectangle is 32 square inches regardless of its dimensions. To find the dimensions, you would typically solve for W using the first equation and then substitute W back into the second equation to find the length.