Final answer:
The width of the sign is 3 inches and the length is 14 inches.
Step-by-step explanation:
To find the dimensions of the sign, we need to set up an equation using the given information. Let's assume that the width of the sign is 'w'. According to the problem, the length of the sign is '3 times the width + 5'. The perimeter of a rectangle is given by the equation P = 2(length + width). We can substitute the given values into this equation and solve for the dimensions of the sign.
So, we have: 2(3w + 5 + w) = 34.
Simplifying the equation, we get: 8w + 10 = 34.
Subtracting 10 from both sides, we get: 8w = 24.
Dividing by 8, we find that the width of the sign is: w = 3.
Substituting this value back into the equation for the length, we get: length = 3(3) + 5 = 14.
Therefore, the dimensions of the sign are: width = 3 inches, length = 14 inches.