Question

zohar is using scissors to cut a rectangle with a length of 5x - 2 and a width of 3x + 1 out of a larger piece of paper. which expression can be used to find the perimeter of the rectangle and what is the perimeter if x = 4? (5x - 2)+(3x + 1); 31 centimeters (5x - 2)+(3x + 1); 36 centimeters 2(5x - 2)+2(3x + 1); 62 centimeters 2(5x - 2)+2(3x + 1); 70 centimeters

Explanation:

Step1: Recall perimeter formula

The perimeter $P$ of a rectangle is $P = 2l+2w$, where $l$ is the length and $w$ is the width. Given $l = 5x - 2$ and $w=3x + 1$, the perimeter expression is $2(5x - 2)+2(3x + 1)$.

Step2: Simplify the expression

\[

$$\begin{align*} 2(5x - 2)+2(3x + 1)&=10x-4 + 6x+2\\ &=(10x+6x)+(-4 + 2)\\ &=16x-2 \end{align*}$$

\]

Step3: Substitute $x = 4$

When $x = 4$, $P=16\times4-2=64 - 2=62$.

Answer:

C. $2(5x - 2)+2(3x + 1)$; 62 centimeters