## Thomas' Calculus 13th Edition

$6+\sqrt{17}+\sqrt{33}$
Apply the distance formula, $d=\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}+(z_{2}-z_{1})^{2}}$ $|AB|=\sqrt{(1-(-1))^{2}+(-1-2)^{2}+(3-1)^{2}}=\sqrt{4+9+4}=\sqrt{17}$ $|AC|=\sqrt{(3-(-1))^{2}+(4-2)^{2}+(5-1)^{2}}=\sqrt{16+4+16}=\sqrt{36}=6$ $|BC|=\sqrt{(3-1)^{2}+(4-(-1))^{2}+(5-3)^{2}}=\sqrt{4+25+4}=\sqrt{33}$ The perimeter is the sum of lengths of the sides $P=6+\sqrt{17}+\sqrt{33}$