Final answer:
To model the rectangle's dimensions, the correct equation is l × w = 12, where l = 2w + 5. This leads to the quadratic equation (2w + 5) × w = 12, which can be used to find the width (w) and the length (l) of the rectangle.
Step-by-step explanation:
The student is asking for the correct equation to model a rectangle where the length (l) is 5 inches longer than twice the width (w), given that the area is 12 square inches. To formulate this equation, we state that l = 2w + 5. Because the area of a rectangle is calculated by multiplying the length by the width, the equation can be expressed as: l × w = 12.
Substituting the expression for l into the area equation, we get (2w + 5) × w = 12. Simplifying this will give a quadratic equation in terms of w, which can be solved to find the dimensions of the rectangle.