Answer:
D. 22
Step-by-step explanation:
To find the perimeter of the rectangle with length of (x-1) and the width of (x+6), we need to find the x-value first by using the area of rectangle formula:
[tex]\boxed{area(A)=length\times width}[/tex]
[tex]18=(x-1)(x+6)[/tex]
[tex]x^2+5x-6=18[/tex]
[tex]x^2+5x-24=0[/tex]
[tex](x+8)(x-3)=0[/tex]
[tex]x=-8\ or\ 3[/tex]
If x = -8, then (x-1) will equal to -9, which is impossible for the length, therefore, x has to equal to 3.
To calculate the perimeter of the rectangle, we use this formula:
[tex]\boxed{perimeter(P)=2\times(length+width)}[/tex]
[tex]\begin{aligned}P&=2[(x-1)+(x+6)]\\&=4x+10\ \Longrightarrow\texttt{ substitute x with 3}\\&=4(3)+10\\&=\bf22\end{aligned}[/tex]