the area of a rectangular wall of a barn is 117 square feet. its length is 4 feet longer than the width. find the length and width of the wall of the barn?

Area is the product of length and width. If you assume the dimensions are integers, you are looking for factors of 117 that differ by 4.

117 = 1*117 = 3*39 = 9*13

These last two factors differ by 4, so we know the dimensions of the barn are ...

... 9 ft wide by 13 ft long