Answer: [tex]\dfrac{7}{3}x-2[/tex]
Step-by-step explanation:
Let x be the width of the rectangle , then the length of the rectangle will be :_
Length = [tex]\dfrac{1}{6}x-1[/tex]
We know that the perimeter of a rectangle is given by :-
[tex]P=2(l+w)[/tex]
Substitute the value of length and width we get,
[tex]P=2(\dfrac{1}{6}x-1+x)[/tex]
Combine like terms, we get
[tex]P=2(\dfrac{1+6}{6}x-1)\\\\\Rightarrow\ P=2(\dfrac{7}{6}x-1)\\\\\Rightarrow\ P=2\times\dfrac{7}{6}x-2\times1\\\\\Rightarrow\ P=\dfrac{7}{3}x-2[/tex]
Hence, the expression represents the perimeter of the rectangle : [tex]\dfrac{7}{3}x-2[/tex]
