SOLUTION
Step1: Write out the given information
[tex]\begin{gathered} \text{perimeter}=58in \\ \text{length}=20\text{ in } \end{gathered}[/tex]Step2: write out the formula
[tex]\text{perimeter}=2(l+w)[/tex]Step3: Substitute the value and find the width of the rectangle
[tex]\begin{gathered} 58=2(20+w) \\ \text{divide both sides by 2} \\ \frac{58}{2}=\frac{2(20+w)}{2} \\ 29=20+w \\ \end{gathered}[/tex]Then
[tex]\begin{gathered} \text{subtract 20 from both sides } \\ 29-20=20-20+w \\ 9=w \\ \text{Hence, the width is 9 in} \end{gathered}[/tex]Step4: Calculate the Area of the Rectangle
[tex]\begin{gathered} \text{Area of rectangle =l}\times w \\ \text{where l=20 and w=9} \\ \text{substitute the value } \\ \text{Area =20}\times9 \\ \text{Area}=180in^2 \end{gathered}[/tex]Therefore the Area of the rectangle is 180 in²
