Question

The length of a rectangle is 3 units shorter than one-third of the width, x.

Answer 1

$\frac{8x}{3} - 6$ is the expression that represents the perimeter of rectangle

Solution:

Let "x" represent the width of rectangle

Given that length of rectangle is 3 units shorter than one-third of the width x

length of rectangle = one-third of the width x - 3

$\text{ length of rectangle} = \frac{1}{3}x - 3 = \frac{x}{3} - 3\\\\\text{ length of rectangle} = \frac{x}{3} - 3$

The perimeter of rectangle is given as:

perimeter of rectangle = 2(length + width)

Substituting the known values we get,

$\text{ perimeter of rectangle }= 2(\frac{x}{3} - 3 + x)\\\\\rightarrow 2(\frac{x - 9 + 3x}{3})\\\\\rightarrow 2(\frac{4x-9}{3})\\\\\rightarrow\frac{8x-18}{3}\\\\\rightarrow\frac{8x}{3} - \frac{18}{3}\\\\\rightarrow\frac{8x}{3} - 6$

Thus perimeter of rectangle is $\frac{8x}{3} - 6$

Thus option 1 is correct