Question

1. a rectangle is pictured with algebraic expressions that represent the lengths of its sides. determine the simplified form of the expression that represents the perimeter of this rectangle.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length} + \text{width}) \). From the diagram, the length is \( 3x - 11 \) and the width is \( x + 9 \).

Step2: Substitute the length and width into the formula

Substitute length \( = 3x - 11 \) and width \( = x + 9 \) into the perimeter formula:
\[
P = 2\times((3x - 11)+(x + 9))
\]

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses:
\[
(3x - 11)+(x + 9)=3x + x- 11 + 9=4x-2
\]

Step4: Multiply by 2 to get the perimeter

Now multiply the simplified expression by 2:
\[
P = 2\times(4x - 2)=8x-4
\]

Answer:

The simplified form of the perimeter expression is \( 8x - 4 \)