in the diagram, wz = √26. what is the perimeter of parallelogram wxyz? 2√26 + 8 units 2√26 + 6 units 2√26 + 4 units 2√26 + 2 units

Question

Accepted Answer

# Explanation:
## Step1: Recall the property of parallelogram
In a parallelogram, $WZ = XY=\sqrt{26}$, $WX = ZY$.
## Step2: Calculate the length of $WX$
Use the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For points $W(-2,4)$ and $X(2,4)$, $x_1=-2,y_1 = 4,x_2=2,y_2 = 4$.
$$
\begin{align*}
WX&=\sqrt{(2-(-2))^2+(4 - 4)^2}\
&=\sqrt{(2 + 2)^2+0^2}\
&=\sqrt{16}\
&=4
\end{align*}
$$
For points $Z(-3,-1)$ and $Y(1,-1)$, $x_1=-3,y_1=-1,x_2=1,y_2=-1$
$$
\begin{align*}
ZY&=\sqrt{(1-(-3))^2+(-1+1)^2}\
&=\sqrt{(1 + 3)^2+0^2}\
&=\sqrt{16}\
&=4
\end{align*}
$$
## Step3: Calculate the perimeter of parallelogram $WXYZ$
The perimeter $P$ of a parallelogram is $P = 2(WZ+WX)$. Since $WZ=\sqrt{26}$ and $WX = 4$
$$
\begin{align*}
P&=2(\sqrt{26}+4)\
&=2\sqrt{26}+8
\end{align*}
$$

# Answer:
$2\sqrt{26}+8$ units

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the property of parallelogram

Step2: Calculate the length of \(WX\)

Step3: Calculate the perimeter of parallelogram \(WXYZ\)

Answer: