The expressions x-1 and x+6 represent the length and width of a rectangle, respectively. If the area of the rectangle is 18, what is the perimeter of the rectangle?

A. 16
B. 18
C. 20
D. 22



Answer :

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]