Question

1. which of the following expressions represents the perimeter of the figure below?

a. 3x - 11
b. 7x - 11
c. 14x - 22
d. 7x - 22
(figure: a rectangle with one side labeled 5x - 4 and another side labeled 2x - 7)

Explanation:

Step1: Recall Perimeter Formula for Rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). Here, the length is \( 5x - 4 \) and the width is \( 2x - 7 \).

Step2: Substitute Length and Width into Formula

Substitute \( l = 5x - 4 \) and \( w = 2x - 7 \) into the perimeter formula:
\( P = 2[(5x - 4) + (2x - 7)] \)

Step3: Simplify Inside the Brackets

Combine like terms inside the brackets:
\( (5x - 4) + (2x - 7) = 5x + 2x - 4 - 7 = 7x - 11 \)

Step4: Multiply by 2

Multiply the simplified expression by 2:
\( P = 2(7x - 11) = 14x - 22 \)

Answer:

C. \( 14x - 22 \)