The area of a rectangular wall of a barn is 154 square feet. Its length is 8 feet longer than twice its width. Find the length and width of the wall of the barn.

Step 1 ：We are given that the area of a rectangular wall of a barn is 154 square feet. Its length is 8 feet longer than twice its width. We need to find the length and width of the wall of the barn.

Step 2 ：We can solve this problem by setting up a system of equations. The area of a rectangle is given by the formula length times width. We know that the area is 154 square feet. We also know that the length is 8 feet longer than twice the width. We can represent this information as two equations: \(length \times width = 154\) and \(length = 2 \times width + 8\).

Step 3 ：Solving this system of equations gives two possible solutions for the length and width: (-14, -11) and (22, 7). However, the dimensions of a wall cannot be negative. Therefore, the only valid solution is (22, 7).

Step 4 ：This means the length of the wall is 22 feet and the width is 7 feet.

Step 5 ：Final Answer: The length of the wall is \(\boxed{22}\) feet and the width is \(\boxed{7}\) feet.