Question

the length of a rectangle is 8 feet, and its area is less than 108 square feet. select an inequality that represents (x) (in feet) of the rectangle. then solve the inequality.

1. (8x<108)
2. (108 < 8x)
3. (8x<108)
4. (2x + 16<108)

Explanation:

1. Analysis of the problem:

• Let the width of the rectangle be \(x\) feet and the length be 16 feet. The area of a rectangle is given by \(A = \text{length}\times\text{width}\), so the area \(A = 16x\) square - feet.
• We are given that the area is less than 108 square - feet.

1. Set up the inequality:

• Since \(A=16x\) and \(A < 108\), we can write the inequality \(16x<108\).

Step1: Identify the area formula

The area of a rectangle \(A = l\times w\), where \(l = 16\) and \(w=x\), so \(A = 16x\).

Step2: Set up the inequality based on the area condition

We know that \(A<108\), substituting \(A = 16x\) gives \(16x<108\).

Answer:

\(16x < 108\) (corresponding to the option that is not fully visible in the image but should be the correct one based on the problem - solving steps)