Final answer:
The correct quadratic equation to find the dimensions of the concrete pad is x² + 11x - 80 = 0. Solving for x, the width is found to be 5 feet and the length is 16 feet.
Step-by-step explanation:
To find the dimensions of the concrete pad, we need to establish variables based on the given conditions. Let's denote the width of the pad as x and the length as x + 11 (since the length is 11 feet more than the width). The area of the concrete pad is given to be 80 ft², so we can create an equation based on these dimensions:
- Area = width × length
- 80 = x × (x + 11)
Expanding the equation and arranging it in standard quadratic form, we get:
- 80 = x² + 11x
- x² + 11x - 80 = 0
This equation matches with option (b) from the provided choices. To find the actual dimensions, we would solve this quadratic equation usually using the quadratic formula, factoring, or completing the square:
- (x + 16)(x - 5) = 0
- x = -16 or x = 5
Since a width cannot be negative, we discard x = -16, leaving x = 5 feet as the width. The length is then 5 + 11 = 16 feet.
Therefore, the dimensions of the concrete pad are 5 feet in width and 16 feet in length.