Question

Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5,0). Find the perimeter of the triangle. Express your answer in simplest radical form.

Answer 1

we must know the measure of each side, for this we must calculate the distance between points

the formula is

`d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}`

AB

`\begin{gathered} \sqrt[]{(-6-(-3))^2+(2-6)^2} \\ \sqrt[]{25} \\ AB=5 \end{gathered}`

AC

`\begin{gathered} \sqrt[]{(-6-5)^2+(2-0)^2} \\ \sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}`

BC

`\begin{gathered} \sqrt[]{(-3-5)^2+(6-0)^2} \\ \\ \sqrt[]{100} \\ BC=10 \end{gathered}`

now add all sides to find the perimeter

`\begin{gathered} 5+5\sqrt[]{5}+10 \\ \end{gathered}`

the perimeter is

`15+5\sqrt[]{5}\approx26.18`