Final answer:
To find the width and the length of the rectangular bulletin board, set up the equation based on given information: 55 = (3W - 4) × W. Solve this quadratic equation to find the width, and then calculate the length. The width is 5 ft, and the length is 11 ft.
Step-by-step explanation:
The area of a rectangular bulletin board is given as 55 ft², and the length (L) is described as four feet less than three times the width (W). Therefore, the relationship between length and width can be expressed as L = 3W - 4. To find the dimensions of the bulletin board, we use the formula for the area of a rectangle, which is Area = Length × Width.
Using the information given:
55 = (3W - 4) × W
55 = 3W² - 4W
3W² - 4W - 55 = 0
This is a quadratic equation that can be solved by factorization or using the quadratic formula. After finding the positive value of the width (since dimensions cannot be negative), the length can be calculated by substituting the width back into the relation L = 3W - 4.
After solving, we would find that the width of the rectangular bulletin board is 5 ft, and the length is 11 ft (since L = 3(5) - 4 = 15 - 4).