Draw the rectangle. Extend one of the sides to indicate "an existing barn" on that side. Label that side, and the opposite side, as "L", noting that L must be no more than 50. Label the two remaining sides as "w".

Note that the fencing indicates the fenced perimeter; the side with the barn will not be counted in this perimeter, so 2w + L = 200.

Solve for L in terms of w. Plug the result into the "area" formula for a rectangle.

Maximize the area, keeping the limits on L in mind. :wink: