Question

The length of a rectangle is one unit shorter than one-sixth of the width, x. Which expression represents the perimeter of the rectangle? 7/3x−2 1/3x−4 1/3x−2 ​ 7/3x−8

Answer 1

Width: x
Length: 1/6x-1
Perimeter
=x+x+1/6x+1/6x-1-1
=14/6x-2
=7/3x-2

Answer 2

Answer: $\dfrac{7}{3}x-2$

Step-by-step explanation:

Let x be the width of the rectangle , then the length of the rectangle will be :_

Length = $\dfrac{1}{6}x-1$

We know that the perimeter of a rectangle is given by :-

$P=2(l+w)$

Substitute the value of length and width we get,

$P=2(\dfrac{1}{6}x-1+x)$

Combine like terms, we get

$P=2(\dfrac{1+6}{6}x-1)\\\\\Rightarrow\ P=2(\dfrac{7}{6}x-1)\\\\\Rightarrow\ P=2\times\dfrac{7}{6}x-2\times1\\\\\Rightarrow\ P=\dfrac{7}{3}x-2$

Hence, the expression represents the perimeter of the rectangle : $\dfrac{7}{3}x-2$