Question

What is the length of side PQ in this figure?

A.4
B.14
C. square root of 52
D.square root of 61

Answer 1

I hope this helps you

Answer 2

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.