The perimeter of the rectangle is
[tex]P=46in[/tex]Let the length of the rectangle be
[tex]=x[/tex]Let the width of the rectangle be
[tex]=y[/tex]The length is 7 in more than the width, can be represented using the equation below
[tex]x=(y+7)in\ldots\ldots\text{.}\mathrm{}(1)[/tex]The perimeter of a rectangle is calculated using the formula below
[tex]\begin{gathered} P=2(Length+breadth) \\ P=2(x+y)\ldots\text{.}(2) \end{gathered}[/tex]Substitute the values of P=46 and equation (1) in equation (2)
[tex]\begin{gathered} P=2(x+y) \\ 46=2(y+7+y) \\ 46=2(y+y+7) \\ 46=2(2y+7) \\ by\text{ expanding the bracket, we will have} \\ 46=4y+14 \\ 4y+14=46 \end{gathered}[/tex]Subtract 14 from both sides
[tex]\begin{gathered} 4y+14=46 \\ 4y+14-14=46-14 \\ 4y=32 \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} 4y=32 \\ \frac{4y}{4}=\frac{32}{4} \\ y=8 \end{gathered}[/tex]Substitute the value of y= 8 in equation (1)
[tex]\begin{gathered} x=y+7 \\ x=8+7 \\ x=15 \end{gathered}[/tex]Therefore,
The length of the rectangle = 15 in
The
