Well, I'm way past the 15 min mark, but here's how to do the question.
With this, you will need to use the distance formula, [tex] \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex], on XY, YZ, and ZX.
XY: [tex] \sqrt{(3-1)^2+(1-6)^2} [/tex]
Firstly, solve inside the parentheses: [tex] \sqrt{(2)^2+(-5)^2} [/tex]
Next, solve the exponents: [tex] \sqrt{4+25} [/tex]
Next, solve the addition, and XY's distance will be √29
(The process is the same with the other 2 sides, so I'll go through them real quickly)
YZ:
[tex] \sqrt{(6-3)^2+(3-1)^2}\\ \sqrt{(3)^2+(2)^2}\\ \sqrt{9+4}\\ \sqrt{13} [/tex]
ZX:
[tex] \sqrt{(1-6)^2+(6-3)^2}\\ \sqrt{(-5)^2+(3)^2}\\ \sqrt{25+9}\\ \sqrt{34} [/tex]
Now that we got the 3 sides, we can add them up: [tex] \sqrt{29}+\sqrt{13} +\sqrt{34} =14.8 [/tex]
In short, your answer is 14.8, or the second option.
