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

Answer 1

The perimeter \( P \) of a rectangle can be calculated using the formula:

\[
P = 2 \times (\text{length} + \text{width})
\]

In this case, the length of the rectangle is \( 5x - 2 \) and the width is \( 3x + 1 \). Thus, the expression for the perimeter becomes:

\[
P = 2 \times \left( (5x - 2) + (3x + 1) \right)
\]

Now, simplifying the expression inside the parentheses:

\[
(5x - 2) + (3x + 1) = 5x + 3x - 2 + 1 = 8x - 1
\]

Therefore, the expression for the perimeter is:

\[
P = 2 \times (8x - 1) = 16x - 2
\]

Now, we need to find the perimeter when \( x = 4 \):

\[
P = 16(4) - 2 = 64 - 2 = 62 \text{ centimeters}
\]

Thus, the final answer is:

**2(5x−2)+2(3x+1); 62 centimeters.**