A rectangle has an area of \( 16 \mathrm{ft}^{2} \). The length is 2 ft longer than the width. Let \( w \) represent the width of the rectangle. Which equation can be used to find the dimensions of this rectangle? A. \( w+2=16 \) B. \( 2 w+2=16 \) C. \( w^{2}+2=16 \) D. \( w^{2}+2 w=16 \)

To find the dimensions of this rectangle, you can start by expressing the length in terms of the width. Since the length is 2 ft longer than the width (\( w \)), we can write the length as \( w + 2 \). The area of a rectangle is given by the formula: Area = Length × Width. Therefore, the equation can be set up as: \[ w(w + 2) = 16 \] When simplified, this results in the quadratic equation: \[ w^2 + 2w = 16 \] --- Did you know that the concept of finding the dimensions of rectangles is rooted in ancient civilizations? The Egyptians and Babylonians were known to use geometric principles for land measurement thousands of years ago! This practice evolved into the sophisticated algebraic techniques we use today to solve such problems. --- If you're tackling this kind of problem, one common mistake is forgetting to set the area formula equal to the value given (16 in this case). Instead, people might mix up the relationships between width and length! Always keep your definitions clear, and remember to double-check the equation you form to avoid that confusion.