The perimeter of a standard-sized rectangular rug is 40 ft . The length is 2 ft longer than the width. Find the dimensions. The width is \( \square \mathrm{ft} \). The length is \( \square \mathrm{fl} \).

To solve for the dimensions of the rug, we can set up the equations based on the perimeter formula for a rectangle, which is \( P = 2(\text{length} + \text{width}) \). Given that the perimeter is 40 ft, we have: \[ 2(\text{length} + \text{width}) = 40 \] Dividing both sides by 2 gives: \[ \text{length} + \text{width} = 20 \] Now, let's denote the width as \( w \). Since the length is 2 ft longer than the width, we can express the length as \( w + 2 \). Plugging this into the equation gives: \[ (w + 2) + w = 20 \] Simplifying this, we have: \[ 2w + 2 = 20 \] Subtracting 2 from both sides results in: \[ 2w = 18 \] Dividing both sides by 2 yields: \[ w = 9 \] Now, substituting back for length: \[ \text{length} = w + 2 = 9 + 2 = 11 \] So the width is 9 ft, and the length is 11 ft. The width is \( 9 \mathrm{ft} \). The length is \( 11 \mathrm{ft} \). The concept of rectangular dimensions has been around for centuries, connecting back to ancient civilizations that needed efficient ways to calculate land area and material use. From the Egyptians building pyramids to today's interior design, understanding how to manage space effectively remains timeless and essential! When working on similar problems, always double-check your equations! A common mistake is misinterpreting relationships, like confusing length and width or overlooking units. Clearly defining your variables at the outset can help you visualize the problem better and avoid confusion!