Question

consider the rectangle depicted below. which of the following computes the perimeter around the rectangle? rectangle with length ( x + 6 ) and width ( x ) options: ( 4x + 12 ), ( 2x + 6 ), ( x^2 + x^6 ), ( x^2 + 6x ), nothing in this list is correct.

Explanation:

Step1: Recall the perimeter formula for a rectangle

The perimeter \( P \) of a rectangle is given by \( P = 2\times(\text{length}+\text{width}) \). Here, the length is \( x + 6 \) and the width is \( x \).

Step2: Substitute the length and width into the formula

Substitute length \( = x + 6 \) and width \( = x \) into the perimeter formula:
\( P = 2\times((x + 6)+x) \)

Step3: Simplify the expression inside the parentheses

First, combine like terms inside the parentheses: \( (x + 6)+x = 2x + 6 \)

Step4: Multiply by 2

Now, multiply the result by 2: \( P = 2\times(2x + 6) \)
Using the distributive property \( a(b + c)=ab+ac \), we get \( P = 2\times2x+2\times6 = 4x + 12 \)

Answer:

\( 4x + 12 \) (corresponding to the option "4x + 12")