Final answer:
To find the width of the walkway, we set up an equation using the area of the garden plus the walkway. Solving this equation leads us to the width of the walkway as 2.67 feet, rounded to 2 feet.
Step-by-step explanation:
The area of a rectangular garden is equal to the product of its length and width. Let's assume the width of the garden is 'w' feet and the length is 'l' feet. Since the outside dimensions of the walkway are 12 feet by 18 feet, we can determine that the overall dimensions of the garden plus the walkway are (l+2w) feet by (w+2w) feet. We know that the area of the garden plus the walkway is 72 square feet, so we can set up the equation (l+2w)(w+2w) = 72.
Simplifying this equation, we get (l+2w)(3w) = 72. Expanding the left side of the equation, we get 3w^2 + 3lw = 72. Rearranging the terms, we have 3w^2 + 3lw - 72 = 0.
Since we're asked to find the uniform width of the walkway, we can solve this quadratic equation for 'w'. We can either factor the equation or use the quadratic formula. Factoring is easier in this case, so we look for two numbers that multiply to -72 and add to 3. The numbers that fit this criteria are 9 and -8. So, we have (w+9)(3w-8) = 0.
Setting each factor to zero, we find two possible values for 'w': w+9 = 0 or 3w-8 = 0. Solving these equations, we get w = -9 or w = 8/3. Since the width cannot be negative, the width of the walkway must be 8/3 feet, which is equivalent to 2 and 2/3 feet or approximately 2.67 feet. Therefore, the correct answer is A. 2 ft.