The perimeter of a rectangle is given by the formula:
[tex]P=2l+2w[/tex]Where l is the length of the rectangle and w is its width. For this rectangle we know two expressions, one of the length and the other for the width:
[tex]\begin{gathered} l=7y+6 \\ w=4y-9 \end{gathered}[/tex]If we substitute these equations into the formula of the perimeter, we get:
[tex]P=2\times(7y+6)+2\times(4y-9)[/tex]Simplifying we get:
[tex]\begin{gathered} P=2\times(7y+6)+2\times(4y-9) \\ P=14y+12+8y-18 \\ P=22y-6 \end{gathered}[/tex]replacing the value of the perimeter (104) and then solving for y we get:
[tex]\begin{gathered} 104=22y-6 \\ 110=22y \\ y=\frac{110}{22}=5 \end{gathered}[/tex]Now that we know that y equals 5, let's replace it into the formulas of the length and width:
[tex]\begin{gathered} l=7\times5+6=41 \\ w=4\times5-9=11 \end{gathered}[/tex]Then, the length equals 41 inches and the width equals 11 inches
