Question 882671
Assuming that one end of the room was completely open. 
Put one end of the pole in the left bottom corner of where you walk in. 
The other end of the pole would be in the right top corner of the opposite wall. 
You can use the Pythagorean theorem. 
First find the diagonal length of the floor.
{{{D^2=12^2+9^2}}}
{{{D^2=144+81}}}
{{{D^2=225}}}
Now use that length and the height of the room to calculate the longest pole.
{{{L^2=D^2+H^2}}}
{{{L^2=225+8^2}}}
{{{L^2=225+64}}}
{{{L^2=289}}}
{{{L=17}}} units long