Question

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

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:

$30.7$