Given:
The length of a rectangle is 9 in. greater than the width.
So, l=9+w
The area is 36 square inches.
To find the dimensions:
Area formula is,
[tex]A=l\times w[/tex]On substitution we get,
[tex]\begin{gathered} 36=(9+w)(w) \\ 36=9w+w^2 \\ w^2+9w-36=0 \\ (w_{}+12)(w-3)=0 \\ w=-12,3 \end{gathered}[/tex]Negative value is negligible.
Hence, the width, w=3 and the length l=9+3=12.
Hence, the dimensions are,
[tex]l=12,w=3[/tex]