Question

consider triangle pqr. what is the length of side qr? 8 units 8√3 units 16 units 16√3 units

Explanation:

Step1: Apply Pythagorean theorem

In right - triangle \(PQR\) with right - angle at \(P\), the Pythagorean theorem states that \(QR^{2}=PQ^{2}+PR^{2}\). Given \(PQ = 8\sqrt{3}\) and \(PR = 8\).

Step2: Calculate \(QR^{2}\)

\[

$$\begin{align*} QR^{2}&=(8\sqrt{3})^{2}+8^{2}\\ &=64\times3 + 64\\ &=192+64\\ &=256 \end{align*}$$

\]

Step3: Find \(QR\)

Take the square - root of \(QR^{2}\). Since \(QR>0\), \(QR=\sqrt{256}=16\).

Answer:

C. 16 units