Final answer:
To maximize the area of a rectangle with a given perimeter, find the dimensions that satisfy the perimeter condition and maximize the product of length and width.
Step-by-step explanation:
To find the dimensions of the rectangle with the largest area among all rectangles with a perimeter of 184, we can use the formula for perimeter: 2(length + width) = 184. Simplifying this equation, we get length + width = 92.
To maximize the area, we need to find the dimensions that satisfy this condition while also maximizing the product of length and width. By trial and error, we can see that when length = 46 and width = 46, the area is maximized at 2116 square units. Therefore, the dimensions of the rectangle with the largest area are 46 units by 46 units.