In right triangle PQR, angle P is a right angle, PQ = $8$ units, and PR = $16$ units. What is the length of side QR?

• A. $8$ units
• B. $\sqrt{192}$ units
• C. $16$ units
• D. $24$ units

Answer: (B)

Verified step by step guidance

1. Identify the right triangle PQR where angle P is the right angle, meaning side QR is the hypotenuse opposite the right angle.
2. Recall the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse (QR) equals the sum of the squares of the other two sides: \(QR^2 = PQ^2 + PR^2\).
3. Substitute the given side lengths into the Pythagorean theorem: \(QR^2 = 8^2 + 16^2\).
4. Calculate the squares of the given sides: \$8^2 = 64\( and \)16^2 = 256\(, so \)QR^2 = 64 + 256$.
5. Add the values and then take the square root of the sum to find the length of side QR: \(QR = \sqrt{64 + 256}\).