A rectangle has a width \( w \) that is 5 units longer than its length \( I \). Which equation expresses the rectangle's area, \( A \) ?

To express the area of the rectangle, we start by defining the length \( l \) and the width \( w \). Given that the width is 5 units longer than the length, we can write: \[ w = l + 5 \] The area \( A \) of a rectangle is calculated by multiplying its length by its width: \[ A = l \times w \] Substituting for \( w \) gives us: \[ A = l \times (l + 5) \] So, the equation that expresses the area of the rectangle is: \[ A = l(l + 5) \] --- The concept of rectangles dates back to ancient civilizations, with evidence found in Egyptian and Mesopotamian mathematics. They used these shapes for agriculture, architecture, and various crafts long before modern shapes and formulas were formalized. It highlights how deeply ingrained geometry is in our lives! If you're ever building a rectangular garden or a picture frame, knowing this formula can save you from frustration! Just remember: the area is length times width, and keeping track of your units is essential. It’s easy to mix them up, but clarity in measurements will help you avoid those pesky miscalculations!