what is the perimeter of this triangle rounded to the nearest tenth of a unit?

Question

Accepted Answer

# Explanation:
## Step1: Identify the coordinates
Assume the vertices of the triangle are $(x_1,y_1)$, $(x_2,y_2)$, $(x_3,y_3)$. From the graph, we can read the coordinates. Let's say the vertices are $(-2, - 2)$, $(6,6)$ and $(4,-6)$.
## Step2: Use the distance formula
The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
For the first - side between $(-2,-2)$ and $(6,6)$:
$$
\begin{align*}
d_1&=\sqrt{(6+2)^2+(6 + 2)^2}\
&=\sqrt{8^2+8^2}\
&=\sqrt{64 + 64}\
&=\sqrt{128}\
&=8\sqrt{2}\approx11.3
\end{align*}
$$
For the second - side between $(6,6)$ and $(4,-6)$:
$$
\begin{align*}
d_2&=\sqrt{(4 - 6)^2+(-6 - 6)^2}\
&=\sqrt{(-2)^2+(-12)^2}\
&=\sqrt{4+144}\
&=\sqrt{148}\
&=2\sqrt{37}\approx12.2
\end{align*}
$$
For the third - side between $(4,-6)$ and $(-2,-2)$:
$$
\begin{align*}
d_3&=\sqrt{(-2 - 4)^2+(-2 + 6)^2}\
&=\sqrt{(-6)^2+4^2}\
&=\sqrt{36 + 16}\
&=\sqrt{52}\
&=2\sqrt{13}\approx7.2
\end{align*}
$$
## Step3: Calculate the perimeter
The perimeter $P=d_1 + d_2+d_3$.
$$
\begin{align*}
P&\approx11.3+12.2 + 7.2\
&=30.7
\end{align*}
$$
# Answer:
$30.7$

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QUESTION IMAGE

Question

Explanation:

Step1: Identify the coordinates

Step2: Use the distance formula

Step3: Calculate the perimeter

Answer: