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

Since $\triangle PQR$ is right-angled at $P$, the formula for the hypotenuse $QR$ is:
$$QR = \sqrt{QP^2 + PR^2}$$

Step2: Substitute given side lengths

Substitute $QP = 8\sqrt{3}$ and $PR = 8$:
$$QR = \sqrt{(8\sqrt{3})^2 + 8^2}$$

Step3: Calculate squared terms

$$(8\sqrt{3})^2 = 8^2 \times (\sqrt{3})^2 = 64 \times 3 = 192$$
$$8^2 = 64$$

Step4: Sum and take square root

$$QR = \sqrt{192 + 64} = \sqrt{256} = 16$$

Answer:

16 units