Question

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

Explanation:

Step1: Identify triangle type

Triangle \( PQR \) is right - angled at \( P \). So we can use the Pythagorean theorem \( c^{2}=a^{2}+b^{2} \), where \( c \) is the hypotenuse (QR in this case), and \( a = 8 \), \( b = 8\sqrt{3} \).

Step2: Apply Pythagorean theorem

\[

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

\]

Step3: Find the length of QR

Take the square root of both sides: \( QR=\sqrt{256}=16 \)

Answer:

16 units