The rule of the area of a rectangle is
[tex]A=W\times H[/tex]W is the width
H is the height
Since the ratio between width and height is 9: 6 and the height is 36 inches, then we will use the ratio method
[tex]\begin{gathered} W\rightarrow H \\ 9\rightarrow6 \\ W\rightarrow36 \end{gathered}[/tex]By using the cross multiplication
[tex]\begin{gathered} W\times6=9\times36 \\ 6W=324 \end{gathered}[/tex]Divide both sides by 6
[tex]\begin{gathered} \frac{6W}{6}=\frac{324}{6} \\ W=54 \end{gathered}[/tex]Then the width of the rectangle is 54 inches
Substitute W by 54 and H by 36 in the rule of the area to find it
[tex]\begin{gathered} A=54\times36 \\ A=1944inches^2 \end{gathered}[/tex]The area of the rectangle is 1944 square inches
