4) playground lukas is walking around the edge of the playground shown. how far will lukas have walked when he finishes one loop around the playground? round to the nearest unit, if necessary.
units

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 points $A(2,7)$ and $B(17,15)$, $x_1 = 2,y_1 = 7,x_2 = 17,y_2 = 15$.
$$
\begin{align*}
AB&=\sqrt{(17 - 2)^2+(15 - 7)^2}\
&=\sqrt{15^2+8^2}\
&=\sqrt{225 + 64}\
&=\sqrt{289}\
&=17
\end{align*}
$$
## Step2: Calculate the length of $BC$
For points $B(17,15)$ and $C(17,7)$, $x_1 = 17,y_1 = 15,x_2 = 17,y_2 = 7$.
$$
\begin{align*}
BC&=\sqrt{(17 - 17)^2+(7 - 15)^2}\
&=\sqrt{0+(- 8)^2}\
&=\sqrt{64}\
&=8
\end{align*}
$$
## Step3: Calculate the length of $CA$
For points $C(17,7)$ and $A(2,7)$, $x_1 = 17,y_1 = 7,x_2 = 2,y_2 = 7$.
$$
\begin{align*}
CA&=\sqrt{(2 - 17)^2+(7 - 7)^2}\
&=\sqrt{(-15)^2+0}\
&=\sqrt{225}\
&=15
\end{align*}
$$
## Step4: Calculate the perimeter
The perimeter $P=AB + BC+CA$. Substitute $AB = 17$, $BC = 8$, $CA = 15$ into the formula.
$$P=17 + 8+15=40$$

# Answer:
$40$

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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 \(CA\)

Step4: Calculate the perimeter

Answer: