Final answer:
To determine the perimeter of the rectangle with a given area and a length to width ratio, we first find the width (6 ft) and the length (18 ft) by solving an equation derived from the area. Then, we use these dimensions to calculate the perimeter, which is 48 ft.
Step-by-step explanation:
The question asks us to find the perimeter of a rectangle given that the length is three times its width and the area is 108 ft2. First, we represent the width as w and the length as 3w (since it is three times the width). The area of a rectangle is found by multiplying the length by the width, which gives us the equation w × 3w = 108.
Solving for w gives us w2 = 36 and thus w = 6 ft. Now we know the width (6 ft) and length (3 × 6 ft = 18 ft). To find the perimeter, we use the formula P = 2l + 2w. Substituting the known values gives us P = 2×18 ft + 2×6 ft = 36 ft + 12 ft = 48 ft. Therefore, the perimeter of the rectangle is 48 ft.