14. The length of a rectangular picture is 5 inches more than three times the width. Find the dimensions of the picture if its perimeter is 74 inches.

Step 1 ：Let the width be denoted as \(w\) and the length as \(l\).

Step 2 ：Write the equations based on the given information: \(l = 3w + 5\) and \(2l + 2w = 74\).

Step 3 ：Solve the system of equations to find the dimensions of the picture.

Step 4 ：Substitute the first equation into the second equation: \(2(3w + 5) + 2w = 74\).

Step 5 ：Simplify the equation: \(6w + 10 + 2w = 74\).

Step 6 ：Combine like terms: \(8w + 10 = 74\).

Step 7 ：Subtract 10 from both sides: \(8w = 64\).

Step 8 ：Divide both sides by 8: \(w = 8\).

Step 9 ：Substitute the value of \(w\) back into the first equation: \(l = 3(8) + 5\).

Step 10 ：Simplify the equation: \(l = 24 + 5\).

Step 11 ：Find the value of \(l\): \(l = 29\).

Step 12 ：Final Answer: The dimensions of the picture are \(\boxed{8}\) inches in width and \(\boxed{29}\) inches in length.