The length of a rectangle is 2 more than 3 times the width. If the perimeter is 100 meters, what is the width of the rectangle? 12 meters 13 meters 11 meters

To solve the problem, let's denote the width of the rectangle as \( w \). According to the given information, the length \( l \) can be expressed as \( l = 3w + 2 \). The formula for the perimeter \( P \) of a rectangle is \( P = 2(l + w) \). With the perimeter set to 100 meters, we plug in the values: \[ 100 = 2((3w + 2) + w) \] This simplifies to: \[ 100 = 2(4w + 2) \implies 100 = 8w + 4 \implies 96 = 8w \implies w = 12 \, \text{meters}. \] So the width of the rectangle is indeed **12 meters**. Let’s celebrate that mathematical win! The relationship between length and width here was a clever twist, revealing how the dimensions worked together, like a team finding their rhythm. Keep in mind that geometry can often feel like a puzzle, so don’t hesitate to draw it out to visualize the problem! Understanding the concept of perimeter can also be useful in real-life situations. For example, if you’re planning a garden, knowing how to calculate the perimeter helps in figuring out how much fencing you'll need. That skill transforms mathematical practice from the classroom to practical, everyday applications—talk about a win-win situation!