Answer:
w = 11
The width is 11 cm.
Step-by-step explanation:
Since we have one of the side lengths the the perimeter, we can set up the equation to solve for perimeter and plug in the values that we are given in the problem and solve for the unknown (w).
Solving:
[tex]\[P = 2l + 2w \]~~(\text{P stands for perimeter})[/tex]
[tex]\text{Where:}\\\begin{itemize} \item \( P \) is the perimeter, \item \( l \) is the length, \item \( w \) is the width.\end{itemize}[/tex]
[tex]\text{Substitute these values into the formula:}\[68 = 2 \times 23 + 2w\]\[2 \times 23 = 46\]Substitute this value into the equation:\[68 = 46 + 2w\]Subtract 46 from both sides:\[68 - 46 = 2w\]Simplify:\[22 = 2w\]Divide both sides by 2:\[\frac{22}{2} = w\]\[w = 11\][/tex]
Therefore, the width of the rectangle is 11 cm.