Explanation
To determine the length of side \( QR \) in the triangle \( QRS \), we use the Pythagorean theorem. However, the answer choices suggest that this is a right triangle scenario. Assuming \( QRS \) is a right triangle with \( QS \) and \( RS \) as the two sides, we can calculate the length of the hypotenuse \( QR \).
Given:
- \( QS = 12 \) cm
- \( RS = 5 \) cm
For a right triangle with \( QR \) as the hypotenuse, the Pythagorean theorem states:
\[
QR^2 = QS^2 + RS^2
\]
Substitute the given values:
\[
QR^2 = 12^2 + 5^2
\]
\[
QR^2 = 144 + 25
\]
\[
QR^2 = 169
\]
\[
QR = \sqrt{169}
\]
\[
QR = 13 \text{ cm}
\]
So, the length of \( QR \) is \( 13 \) cm.
The correct answer is C. 13 cm.