Question

the dimensions of a rectangle are -9x - 4 and -x - 2. write the simplified expression for the rectangles perimeter.

Explanation:

Step1: Recall the perimeter formula for a rectangle.

The perimeter \( P \) of a rectangle with length \( l \) and width \( w \) is given by \( P = 2(l + w) \). Here, \( l=-9x - 4 \) and \( w=-x - 2 \).

Step2: Substitute the length and width into the formula.

\[

$$\begin{align*} P&=2[(-9x - 4)+(-x - 2)]\\ \end{align*}$$

\]

Step3: Combine like terms inside the brackets.

First, combine the \( x \)-terms: \( -9x+(-x)=-9x - x=-10x \).
Then, combine the constant terms: \( -4+(-2)=-4 - 2=-6 \).
So, the expression inside the brackets becomes \( -10x - 6 \).

Step4: Multiply the result by 2.

\[

$$\begin{align*} P&=2(-10x - 6)\\ &=2\times(-10x)+2\times(-6)\\ &=-20x-12 \end{align*}$$

\]

Answer:

The simplified expression for the rectangle's perimeter is \(-20x - 12\).