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5 days ago

What is the length of side PQ in this figure?

Mathematics

2 answers:

Svet_ta [4.2K]5 days ago

7 0

Response:

Option: C

Detailed explanation:

To determine the length of side PQ, we must first calculate the length of the vertical line segment that is perpendicular to side PR, which we shall call QS.

Since ΔQSR is a right triangle, and we know the lengths of sides QR and SR, we can apply the Pythagorean theorem:

$QR^{2}=SR^{2}+QS^{2}$

$5^{2}=3^{2}+QS^{2}\\ \\QS^{2}=5^{2}-3^{2}\\\\QS^{2}=25-3=16=4^2$

Thus, QS=4.

Next, we analyze ΔQSP, which is also a right triangle, and again utilize the Pythagorean theorem:

$PQ^{2}=QS^{2}+PS^{2}\\ \\PQ^{2}=4^{2}+6^{2}=16+36=52$

This implies $QS=\sqrt{52}=2\sqrt{13}$

Consequently, side PQ measures $\sqrt{52}=2\sqrt{13}$ .

Therefore, option C is the correct choice.

lawyer [3.9K]5 days ago

5 0

I trust this will assist you.

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