Answer:
• Length = 33½ units
,• Width = 33½ units
Explanation:
The perimeter of the rectangle = 134
[tex]\begin{gathered} \text{Perimeter}=2(L+W) \\ 134=2(L+W) \\ L+W=67 \\ \implies L=67-W \end{gathered}[/tex]Using the formula for area:
[tex]\begin{gathered} Area=L\times W \\ =W(67-W) \\ A=67W-W^2 \end{gathered}[/tex]The maximum dimension will occur at the point where the derivative is 0.
[tex]\begin{gathered} A^{\prime}=67-2W=0 \\ 2W=67 \\ W=\frac{67}{2} \\ W=33\frac{1}{2}\text{ units} \end{gathered}[/tex][tex]\begin{gathered} L=67-W \\ =67-33.5 \\ =33\frac{1}{2}\text{ units} \end{gathered}[/tex]The area is maximum when the width and the length are 33½ units.
