Final answer:
The correct width for the garden, based on the given options, is 20 feet. When including a 2-foot-wide walkway around the garden, the total dimensions become 24 feet by 44 feet, resulting in the area of the garden including walkway as 1,056 square feet.
Step-by-step explanation:
The student is working on a problem related to rectangular gardens and how to calculate areas with given dimensions and additional features such as walkways. The expressions given for the area of the garden including a walkway as well as for the area of the walkway only are correct.
The width of the garden should be 20 feet because when you add the 2-foot-wide walkway around the garden, the total width becomes 24 feet, and the total length becomes twice the garden width plus the walkway on both sides, which is 44 feet. The area including the walkway thus becomes (20 + 4)(2×20 + 4) = 24×44 = 1,056 square feet. The area of the garden alone, without the walkway, is 20×40 = 800 square feet. Therefore, the area of the walkway only is 1,056 - 800 = 256 square feet.
To determine the dimensions of the walkway, we can use the expression (2w + 4)(w + 4) - (2w)(w) and plug in the width of the garden as 100 feet to get the area of the walkway, which results in 1,200 square feet. Since this is not one of the options provided, it seems there is a typographical error in the baseline values provided, and the correct width that matches the options would be 20 feet.