The width of the shed floor is 9 feet and the length is 12 feet, calculated by using the area of the rectangle and the given relationship between the length and width.
The student wants to find the width and length of a rectangular shed floor that has an area of 108 square feet. The length of the shed is given as 6 feet less than twice the width. To solve this, let the width be represented as 'w' and the length as 'l'. The area of a rectangle is found by multiplying the length by the width (area = length × width).
According to the problem, l = 2w - 6. Since the area is 108 sq ft, we can set up the equation 108 = w × (2w - 6). Expanding and solving the quadratic equation gives us the dimensions of the shed floor:
- 108 = 2w^2 - 6w
- 0 = 2w^2 - 6w - 108
- Divide all terms by 2.
- 0 = w^2 - 3w - 54
- Factor the quadratic equation.
- (w - 9)(w + 6) = 0
- The width w can be 9 or -6, but since width can't be negative, w = 9 ft.
- Find the length: l = 2w - 6 = 2(9) - 6 = 18 - 6 = 12 ft.
The dimensions of the shed floor are 9 feet in width and 12 feet in length.