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,
, on XY, YZ, and ZX.
XY: ![\sqrt{(3-1)^2+(1-6)^2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%283-1%29%5E2%2B%281-6%29%5E2%7D%20)
Firstly, solve inside the parentheses: ![\sqrt{(2)^2+(-5)^2}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%282%29%5E2%2B%28-5%29%5E2%7D%20)
Next, solve the exponents: ![\sqrt{4+25}](https://tex.z-dn.net/?f=%20%5Csqrt%7B4%2B25%7D%20)
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:
![\sqrt{(6-3)^2+(3-1)^2}\\ \sqrt{(3)^2+(2)^2}\\ \sqrt{9+4}\\ \sqrt{13}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%286-3%29%5E2%2B%283-1%29%5E2%7D%5C%5C%20%5Csqrt%7B%283%29%5E2%2B%282%29%5E2%7D%5C%5C%20%5Csqrt%7B9%2B4%7D%5C%5C%20%5Csqrt%7B13%7D%20)
ZX:
![\sqrt{(1-6)^2+(6-3)^2}\\ \sqrt{(-5)^2+(3)^2}\\ \sqrt{25+9}\\ \sqrt{34}](https://tex.z-dn.net/?f=%20%5Csqrt%7B%281-6%29%5E2%2B%286-3%29%5E2%7D%5C%5C%20%5Csqrt%7B%28-5%29%5E2%2B%283%29%5E2%7D%5C%5C%20%5Csqrt%7B25%2B9%7D%5C%5C%20%5Csqrt%7B34%7D%20)
Now that we got the 3 sides, we can add them up: ![\sqrt{29}+\sqrt{13} +\sqrt{34} =14.8](https://tex.z-dn.net/?f=%20%5Csqrt%7B29%7D%2B%5Csqrt%7B13%7D%20%2B%5Csqrt%7B34%7D%20%3D14.8%20)
In short, your answer is 14.8, or the second option.