Answer:
PN = 6√2 in
PQ = 6√6 in
PR = 6√3 in
Step-by-step explanation:
Please see the attached image where the triangle and the known values are labeled.
From Right triangle altitude theorem, we have
[tex]PN=\sqrt{QN\cdot NR}\\PN=\sqrt{12\cdot6}\\PN=6\sqrt2[/tex]
Now, in right angle triangle PNQ
[tex]PQ=\sqrt{(6\sqrt2)^2+12^2}\\PQ=\sqrt{72+144}\\PQ=\sqrt{216}\\PQ=6\sqrt6[/tex]
Similarly, in triangle PNR,
[tex]PR=\sqrt{(6\sqrt2)^2+6^2}\\PQ=\sqrt{72+36}\\PQ=\sqrt{108}\\PQ=6\sqrt3[/tex]
Therefore, we have
PN = 6√2 in
PQ = 6√6 in
PR = 6√3 in
