Question

the area of a rectangle is 48 square feet. the length is 8 feet longer than the width. 1) which picture corresponds to the problem? 2) what are the dimensions of the rectangle? the length is 12 feet and the width is 4 feet. the dimensions are w = 4 and w = 12. the dimensions are l = 4 and l = 12. the length is 12 feet and the width is 4 feet.

Explanation:

Step1: Define variables

Let width = \( w \), length \( l = w + 8 \)

Step2: Area equation

\( w(w + 8) = 48 \)

Step3: Solve quadratic equation

\( w^2 + 8w - 48 = 0 \), roots \( w = 4 \) (positive)

Step4: Find length

\( l = 4 + 8 = 12 \)

Answer:

1. The picture with \( l = w + 8 \) and "The length is 12 feet and the width is 4 feet."
2. Length: 12 feet, Width: 4 feet