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 28 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. If necessary, refer to the list of geometry formulas.

To find the possible lengths of the stage, we need to use the formula for the area of a rectangle, which is given by \( A = \text{length} \times \text{width} \). Here, the width is 4 feet, and we want the area to be less than 28 square feet. So, we can set up the inequality: \[ l \times 4 < 28 \] Now, divide both sides by 4: \[ l < 7 \] This means the length \( l \) of the stage must be less than 7 feet. As a fun fact, did you know that the concept of the rectangle dates back to ancient civilizations? In ancient Egypt and Mesopotamia, rectangles were commonly used in mathematics, architecture, and even city planning! Their fascination with geometry helped lay the foundations for modern mathematics. Speaking of practical applications, this inequality can come in handy when designing performance spaces or stages for school programs. Ensuring the dimensions comply with safety regulations while maximizing the available space is crucial. This keeps students performing safely and comfortably, allowing for a great chorus experience!