Final answer:
To find the width of the rectangle, we set up an equation based on the area (36 square feet) and the given relationship between width and length (width is 4 times the length). Solving for the length we get 3 feet, and multiplying by 4 gives us the width, which is 12 feet.
Step-by-step explanation:
The question asks for the width of a rectangle given that the area is 36 square feet and the width is 4 times longer than the length. To solve this, we will let 'l' represent the length and 'w' represent the width. Since we know the width is 4 times longer than the length, we can say that w = 4l. We are also given the area of the rectangle, which is 36 square feet. The area of a rectangle is calculated by multiplying the length by the width (A = l × w).
Substituting our formula for the width into the area formula gives us:
A = l × (4l),
36 = 4l².
To find the value of l, we will divide both sides by 4:
l² = 9,
l = 3 (since length cannot be negative).
To find the width, we'll multiply the length by 4:
w = 4l,
w = 4 × 3,
w = 12 feet.
Therefore, the width of the rectangle is 12 feet, which corresponds to option B.