We are given a rectangle that has a width "x" and a length that is one unit shorter than one-sixth of its length. This rectangle can be visualized in the following diagram:
The perimeter of a rectangle is the sum of all of its sides, therefore, the perimeter is given by:
[tex]P=x+x+\frac{x}{6}-1+\frac{x}{6}-1[/tex]
Adding like terms:
[tex]P=2x+\frac{2x}{6}-2[/tex]
Adding the fractions we get:
[tex]P=\frac{14x}{6}-2[/tex]
Simplifying the fraction we get:
[tex]P=\frac{7x}{3}-2[/tex]
And thus we get the expression for the perimeter of the given rectangle.
