Question

a school is building a rectangular stage for its chorus. the stage must have a width of 4 feet. the area of the stage must be less than 20 square feet. (these are rules of the local fire department.) write an inequality that describes the possible lengths (in feet) of the stage. use l for the length of the rectangular stage.

Explanation:

Step1: Recall area of rectangle

The area \( A \) of a rectangle is given by \( A = \text{length} \times \text{width} \). Here, width is 4 feet and length is \( l \), so \( A = 4l \).

Step2: Set up the inequality

The area must be less than 20 square feet. So, \( 4l < 20 \).

Answer:

\( 4l < 20 \) (which can also be simplified to \( l < 5 \) by dividing both sides by 4, but the inequality from the area formula is \( 4l < 20 \))