Given in the question
[tex]\text{Area}_{RECTANGLE}=54in^2[/tex]
The length of the rectangle is
[tex]l=3(n-1)=3n-3[/tex]
The breadth of the rectangle is
[tex]b=n+2[/tex]
The formula for the Area of a rectangle is
[tex]\begin{gathered} \text{Area}_{RECTANGLE}=\text{length}\times breadth \\ \text{Area}_{RECTANGLE}=l\times b \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} \text{Area}_{RECTANGLE}=(3n-3)\times(n+2) \\ (3n-3)\times(n+2)=54 \end{gathered}[/tex]
By expanding the brackets, we will have
[tex]\begin{gathered} (3n-3)\times(n+2)=54 \\ 3n(n+2)-3(n+2)=54 \\ 3n^2+6n-3n-6=54 \\ 3n^2+3n-6-54=0 \\ 3n^2+3n-60=0 \end{gathered}[/tex]
Therefore,
The final answer is = 3n² + 3n - 60 = 0
By factorizing the equation, we will have n^
