Respuesta :
[tex]\frac{8x}{3} - 6[/tex] 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
[tex]\text{ length of rectangle} = \frac{1}{3}x - 3 = \frac{x}{3} - 3\\\\\text{ length of rectangle} = \frac{x}{3} - 3[/tex]
The perimeter of rectangle is given as:
perimeter of rectangle = 2(length + width)
Substituting the known values we get,
[tex]\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[/tex]
Thus perimeter of rectangle is [tex]\frac{8x}{3} - 6[/tex]
Thus option 1 is correct
