Question

select all the correct answers. what is the length of side pq in this figure? a. 4 b. 14 c. $sqrt{52}$ d. $sqrt{61}$

Explanation:

Step1: Apply Pythagorean theorem

Let the height from Q to PR be h. First, find h using right - triangle with side lengths 3 and 5. By Pythagorean theorem $h=\sqrt{5^{2}-3^{2}}=\sqrt{25 - 9}=\sqrt{16}=4$.

Step2: Find length of PQ

In right - triangle with base 6 and height 4, by Pythagorean theorem $PQ=\sqrt{6^{2}+4^{2}}=\sqrt{36 + 16}=\sqrt{52}$.

Answer:

C. $\sqrt{52}$