The length of a rectangle is 4 inches more than its width, and its perimeter is 34 inches. Find the length and width of the rectangle. Find the width of the rectangle. 7.5 in . 6 in . 6.5 in .

To find the width of the rectangle, let's denote the width as \( w \). According to the problem, the length \( l \) can be expressed as \( l = w + 4 \). The formula for perimeter is \( P = 2l + 2w \). Given that the perimeter is 34 inches, we can set up the equation: \[ 2(w + 4) + 2w = 34 \] Simplifying, we have: \[ 2w + 8 + 2w = 34 \] \[ 4w + 8 = 34 \] \[ 4w = 26 \] \[ w = 6.5 \] Thus, the width of the rectangle is 6.5 inches! Now, to find the length, substitute \( w \) back into the length equation: \[ l = 6.5 + 4 = 10.5 \] So, the rectangle has a width of 6.5 inches and a length of 10.5 inches. The dimensions of the rectangle are often a source of confusion, but here's a fun fact: the rectangle is one of the simplest shapes studied in geometry and is used in architecture, design, and engineering. Having fun while building or crafting projects often involves forming rectangular shapes which can lead to beautiful creations! When solving such equations, it's common to set up the relationships between various parts of the problem. Make sure to clearly define your variables, as it helps you avoid mistakes. A common error is to miscalculate when combining like terms or misrepresent the equations' relationships, so double-checking your work is always a good practice!