Answer:
c) 676 sq. ft.
Step-by-step explanation:
With the 24 ft barn, the total perimeter can be 24+80 = 104 feet. This allows the farmer to make a square pen 104/4 = 26 feet on a side, for an area of ...
(26 ft)² = 676 ft²
_____
Comment on "fence" problems
These fence problems have different solutions for different ratios of "barn" length to "fence" length. When the barn length is more than 1/2 the length of the fence, the optimum shape is a rectangle in which half the fence is used parallel to the barn. (The full length of the barn is not used.)
When the barn length is between 1/2 and 1/3 the fence length, the optimum shape is a rectangle with one side equal to the barn length.
When the barn length is less than 1/3 the fence length, as here, the optimum shape is a square, with the barn side being augmented by fence as required. Here, 2 ft of fence is added to the 24 ft barn to make a square 26 ft on each side.
