Question

the length of a rectangle is 2 ft shorter than 5 times its width, x. the area of the rectangle is less than 100 ft². which inequality can be used to determine the maximum width (ft) of the rectangle? a. 5x² - 2x < 100 b. 5x² - 2x > 100 c. 5x² + 2x > 100 d. 5x² + 2x < 100

Explanation:

Step1: Define length in terms of width

The width is \( x \). The length is 2 ft shorter than 5 times the width, so length \( l = 5x - 2 \).

Step2: Recall area formula for rectangle

The area \( A \) of a rectangle is \( A = \text{length} \times \text{width} \). Substituting length and width, we get \( A = x(5x - 2) \).

Step3: Expand and apply inequality

Expanding \( x(5x - 2) \) gives \( 5x^2 - 2x \). The area is less than \( 100 \, \text{ft}^2 \), so the inequality is \( 5x^2 - 2x < 100 \).

Answer:

A. \( 5x^2 - 2x < 100 \)