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?\
\bigcirc\\ (5x-2)+(3x+1); 31 centimeters\
\bigcirc\\ (5x-2)+(3x+1); 36 centimeters\
\bigcirc\\ 2(5x-2)+2(3x+1); 62 centimeters\
\bigcirc\\ 2(5x-2)+2(3x+1); 70 centimeters

Explanation:

Step1: Recall Perimeter Formula

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \), or equivalently \( P = 2\times\text{length}+2\times\text{width} \). Here, length is \( 5x - 2 \) and width is \( 3x + 1 \), so the perimeter expression should be \( 2(5x - 2)+2(3x + 1) \). This eliminates the first two options.

Step2: Substitute \( x = 4 \)

Substitute \( x = 4 \) into \( 2(5x - 2)+2(3x + 1) \):

• First, calculate \( 5x - 2 \) when \( x = 4 \): \( 5(4)-2=20 - 2 = 18 \)
• Then, calculate \( 3x + 1 \) when \( x = 4 \): \( 3(4)+1=12 + 1 = 13 \)
• Now, find the perimeter: \( 2(18)+2(13)=36 + 26 = 62 \)

Answer:

C. \( 2(5x - 2)+2(3x + 1) \); 62 centimeters (assuming the third option is labeled C, if not, the option with \( 2(5x - 2)+2(3x + 1) \) and 62 centimeters)