A rectangle is three times as long as it is wide. The perimeter is 40 feet. Find the width.

To find the width of the rectangle, let's denote the width as \( w \). Since the rectangle is three times as long as it is wide, the length will be \( 3w \). The formula for the perimeter \( P \) of a rectangle is given by: \[ P = 2(\text{length} + \text{width}) \] Substituting the known values, we have: \[ 40 = 2(3w + w) \] This simplifies to: \[ 40 = 2(4w) \] \[ 40 = 8w \] Now, dividing both sides by 8: \[ w = 5 \] So, the width of the rectangle is 5 feet. Now, let’s take a fun stroll down memory lane. The concept of rectangles dates back to ancient civilizations, where they were used for planning fields and constructing buildings. The Egyptians famously utilized geometric principles, evident in the design of the pyramids. Fast forward to today, rectangles are everywhere—from cell phones to tables to buildings—shaping the very layout of our modern lives. And speaking of those everyday shapes, here’s a tip: always double-check your perimeter calculations! A common mistake is miscalculating the length and width when setting up equations. Remember, a rectangle’s perimeter is all about the sum of all sides, so keep an eye out for those pesky reference values, and you’ll ace your geometry problems!