Final: The Rug, Modeled

A word problem about a rectangle can lead to a quadratic equation. Write the equation first, and solve it later.

The area of a rectangle is width times length. If a rectangle is $x$ meters wide and its length is 2 meters more than its width, the length is $x+2$. If its area is 15 square meters, the equation is $x\left(x+2\right) = 15$. Keep the product of the width and the length as it is. Expanding it is a solving step, not a modeling step. The equation says the same thing as the story, with the width as the unknown.