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 given by \( P = 2\times(\text{length}+\text{width}) \), which expands to \( P = 2\times\text{length}+2\times\text{width} \). For length \( 5x - 2 \) and width \( 3x + 1 \), the perimeter expression is \( 2(5x - 2)+2(3x + 1) \). So we eliminate the first two options.

Step2: Substitute \( x = 4 \)

First, simplify the perimeter expression:
\( 2(5x - 2)+2(3x + 1)=10x - 4 + 6x + 2 = 16x - 2 \).

Now substitute \( x = 4 \):
\( 16(4)-2 = 64 - 2 = 62 \).

Answer:

\( 2(5x - 2)+2(3x + 1) \); 62 centimeters (the third option)