10 POINTS!!
What is the length of side PQ in this figure?

C

Step-by-step explanation:

o 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.

plz mark brainliest

2nd one in the first row is correct