Final answer:
To find the length of the trampoline, we can set up an equation using the given information. The width of the trampoline can be represented as x ft. The length is 3 ft more than thrice the width. By solving the equation, we find that the length of the trampoline is 17 ft.
Step-by-step explanation:
To find the length of the trampoline, we can set up an equation using the given information. Let's say the width of the trampoline is x ft. According to the problem, the length is 3 ft more than thrice the width, so the length can be represented as 3x + 3 ft. The area of the trampoline is given as 126 ft², so we have the equation: x(3x + 3) = 126. Simplifying this equation, we get: 3x² + 3x - 126 = 0. Now, we can factor or use the quadratic formula to solve for x. By factoring, we get (x + 9)(3x - 14) = 0. Setting each factor equal to zero, we find two possible values for x: x = -9 or x = 14/3. Since the width of a trampoline cannot be negative, we discard the -9. Therefore, the width of the trampoline is x = 14/3 ft. Finally, we can calculate the length using the equation from before: length = 3x + 3 = 3(14/3) + 3 = 14 + 3 = 17 ft. So, the correct answer is d) 17 ft.