Question

traffic signs are regulated by the manual on uniform traffic control devices (mutcd). the perimeter of a rectangular traffic sign is 116 inches. also, its length is 12 inches longer than its width. find the dimensions of this sign.
what is the length of the sign?
the length of the sign is 35 in.
what is the width of the sign?
the width of the sign is

Explanation:

Step1: Define variables

Let the width of the rectangle be \( w \) inches. Then the length \( l \) is \( w + 12 \) inches (since length is 12 inches longer than width).

Step2: Use perimeter formula

The perimeter \( P \) of a rectangle is given by \( P = 2(l + w) \). We know \( P = 116 \) inches. Substitute \( l = w + 12 \) into the formula:
\[
116 = 2((w + 12) + w)
\]

Step3: Simplify the equation

First, simplify the expression inside the parentheses:
\[
116 = 2(2w + 12)
\]
Then divide both sides by 2:
\[
58 = 2w + 12
\]

Step4: Solve for \( w \)

Subtract 12 from both sides:
\[
58 - 12 = 2w
\]
\[
46 = 2w
\]
Divide both sides by 2:
\[
w = \frac{46}{2} = 23
\]
(We can also find width by subtracting 12 from length: \( 35 - 12 = 23 \) since length is 35 inches as given.)

Answer:

The width of the sign is 23 in.