Answer:
option: C
Step-by-step explanation:
To find the side PQ ; we need to first find the length of the given line segment which is perpendicular to side PR; let name it as QS.
Now as ΔQSR is an right angled triangle.
and the length of the side QR and SR is given , so using Pythagorean theorem we have
\(QR^{2}=SR^{2}+QS^{2}\)
\(5^{2}=3^{2}+QS^{2}\\ \\QS^{2}=5^{2}-3^{2}\\\\QS^{2}=25-3=16=4^2\)
⇒ QS=4
Now again ΔQSP is an right angled triangle; so using Pythagorean theorem in ΔQSP we have
\(PQ^{2}=QS^{2}+PS^{2}\\ \\PQ^{2}=4^{2}+6^{2}=16+36=52\)
This means \(QS=\sqrt{52}=2\sqrt{13}\)
Hence, the length of side PQ is \(\sqrt{52}=2\sqrt{13}\).
Hence, option C is correct.
