The perimeter of the rectangle is
[tex]=24[/tex]The length is
[tex]=y[/tex]The width is
[tex]=x[/tex]The formula to calculate the perimeter of a rectangle is given as
[tex]=2(\text{length}+\text{width)}[/tex]By substituting the values of the length, width, and perimeter above we will get the equation below
[tex]\begin{gathered} perimeter=2(\text{length}+\text{width)} \\ 2(y+x)=24 \end{gathered}[/tex]To talk about the length y in terms of x, we will make y the subject of the formula in the equation above
[tex]\begin{gathered} 2(y+x)=24 \\ \text{divide both sides by 2} \\ \frac{2(y+x)}{2}=\frac{24}{2} \\ y+x=12 \\ \text{therefore,} \\ y=12-x \end{gathered}[/tex]Hence,
The length y in terms of x is given as y=12-x
To calculate the possible values of x and the possible values of y
The sum of x and y must give 12 therefore,
[tex]\begin{gathered} \text{when x= 1} \\ y=12-x \\ y=12-1=11 \\ x=1,y=11 \end{gathered}[/tex][tex]\begin{gathered} \text{when x=2} \\ y=12-x \\ y=12-2 \\ y=10 \end{gathered}[/tex][tex]\begin{gathered} \text{when x=3} \\ y=12-x \\ y=12-3 \\ y=9 \end{gathered}[/tex][tex]\begin{gathered} \text{when x=4} \\ y=12-x \\ y=12-4 \\ y=8 \end{gathered}[/tex][tex]undefined[/tex]