Final answer:
To find the dimensions of the given rectangle, assign the width as w and set up an equation using the area and the relationship between length and width. Solve the quadratic equation to find w, and then use it to calculate the length.
Step-by-step explanation:
To find the dimensions of the rectangle, let's let the width be represented as w feet. Then, according to the problem, the length is 5 feet more than twice the width, which can be written as 2w + 5 feet. The area of the rectangle, which is length × width, is given to be 42 square feet.
Factoring the quadratic equation, we find the possible values for w. After finding the width, we substitute back into 2w + 5 to find the length. Ensuring we only take the positive value since dimensions cannot be negative, the dimensions of the rectangle are found.