choose 1 answer: 39.0 40.2 41.4 42.6

Question

Accepted Answer

# Explanation:
## Step1: Calculate the length of $AB$
Use the distance formula $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. For $A(-6,0)$ and $B(4,5)$, $x_1=-6,y_1 = 0,x_2 = 4,y_2=5$.
$$
\begin{align*}
AB&=\sqrt{(4-(-6))^2+(5 - 0)^2}\
&=\sqrt{(10)^2+(5)^2}\
&=\sqrt{100 + 25}\
&=\sqrt{125}\approx11.18
\end{align*}
$$
## Step2: Calculate the length of $BC$
For $B(4,5)$ and $C(8,-3)$, $x_1 = 4,y_1=5,x_2=8,y_2=-3$.
$$
\begin{align*}
BC&=\sqrt{(8 - 4)^2+(-3-5)^2}\
&=\sqrt{(4)^2+(-8)^2}\
&=\sqrt{16 + 64}\
&=\sqrt{80}\approx8.94
\end{align*}
$$
## Step3: Calculate the length of $CD$
For $C(8,-3)$ and $D(-2,-8)$, $x_1=8,y_1=-3,x_2=-2,y_2=-8$.
$$
\begin{align*}
CD&=\sqrt{(-2 - 8)^2+(-8+3)^2}\
&=\sqrt{(-10)^2+(-5)^2}\
&=\sqrt{100+25}\
&=\sqrt{125}\approx11.18
\end{align*}
$$
## Step4: Calculate the length of $DA$
For $D(-2,-8)$ and $A(-6,0)$, $x_1=-2,y_1=-8,x_2=-6,y_2=0$.
$$
\begin{align*}
DA&=\sqrt{(-6+2)^2+(0 + 8)^2}\
&=\sqrt{(-4)^2+(8)^2}\
&=\sqrt{16+64}\
&=\sqrt{80}\approx8.94
\end{align*}
$$
## Step5: Calculate the perimeter
Perimeter $P=AB + BC+CD + DA$.
$$
\begin{align*}
P&=11.18+8.94+11.18+8.94\
&=(11.18\times2)+(8.94\times2)\
&=22.36+17.88\
&=40.24\approx40.2
\end{align*}
$$

# Answer:
B. $40.2$

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QUESTION IMAGE

Question

Explanation:

Step1: Calculate the length of \(AB\)

Step2: Calculate the length of \(BC\)

Step3: Calculate the length of \(CD\)

Step4: Calculate the length of \(DA\)

Step5: Calculate the perimeter

Answer: