Step 1 :Let's denote the width of the sign as \(x\) (in inches). According to the problem, the length of the sign is \(x + 15\) inches.
Step 2 :The perimeter of a rectangle is given by the formula \(2*(length + width)\). In this case, the perimeter is 122 inches. So we can set up the following equation: \(2*(x + (x + 15)) = 122\).
Step 3 :First, simplify the equation: \(2*(2x + 15) = 122\) which simplifies to \(4x + 30 = 122\).
Step 4 :Next, subtract 30 from both sides of the equation: \(4x = 122 - 30\) which simplifies to \(4x = 92\).
Step 5 :Finally, divide both sides by 4 to solve for \(x\): \(x = 92 / 4\) which simplifies to \(x = 23\).
Step 6 :So, the width of the sign is \(23\) inches.
Step 7 :The length of the sign is \(x + 15 = 23 + 15 = 38\) inches.
Step 8 :Therefore, the length of the sign is \(\boxed{38}\) inches.