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 in². in. in³.

Explanation:

Step1: Define variables

Let the width of the sign be \( w \) inches. Then the length \( l = w + 12 \) inches. The perimeter of a rectangle is given by \( P = 2(l + w) \). We know the perimeter \( P = 116 \) inches (assuming the perimeter value is 116 as it seems a typo in the original, likely 116 instead of 11).

Step2: Substitute into perimeter formula

Substitute \( l = w + 12 \) and \( P = 116 \) into \( P = 2(l + w) \):
\[
116 = 2((w + 12) + w)
\]

Step3: Simplify the equation

First, simplify 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:
\[
2w = 58 - 12 = 46
\]
Divide both sides by 2:
\[
w = 23
\]

Step5: Find the length

Since \( l = w + 12 \), substitute \( w = 23 \):
\[
l = 23 + 12 = 35
\]

Answer:

The length of the sign is \(\boldsymbol{35}\) in.