Question

the length of a rectangle is 3 units shorter than one - third of the width, x. which expression represents the perimeter of the rectangle?
○ $\frac{2}{3}x - 8$
○ $\frac{8}{3}x - 2$
○ $\frac{2}{3}x - 4$
○ $\frac{8}{3}x - 6$

Explanation:

Step1: Find the length expression

The length $l$ is 3 units shorter than one - third of the width $x$. So, $l=\frac{1}{3}x - 3$.

Step2: Recall the perimeter formula

The perimeter $P$ of a rectangle is $P = 2(l + w)$, where $w=x$ (width) and $l=\frac{1}{3}x - 3$ (length).

Step3: Substitute length and width into the formula

$P=2((\frac{1}{3}x - 3)+x)$.

Step4: Simplify the expression inside the parentheses

$(\frac{1}{3}x - 3)+x=\frac{1}{3}x+x - 3=\frac{1}{3}x+\frac{3}{3}x - 3=\frac{4}{3}x - 3$.

Step5: Multiply by 2

$P = 2(\frac{4}{3}x - 3)=2\times\frac{4}{3}x-2\times3=\frac{8}{3}x - 6$.

Answer:

$\frac{8}{3}x - 6$