Question

consider triangle pqr. what is the length of side qr?
8 units
8√3 units
16 units
16√3 units
(image of right triangle pqr with right angle at p, pq = 8√3, pr = 8)

Explanation:

Step1: Apply Pythagorean theorem

Since $\triangle PQR$ is right-angled at $P$, the hypotenuse $QR$ can be found using $QR^2 = QP^2 + PR^2$.

Step2: Substitute given side lengths

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

Step3: Calculate each squared term

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

Step4: Sum the squared terms

$$QR^2 = 192 + 64 = 256$$

Step5: Take square root of sum

$$QR = \sqrt{256} = 16$$

Answer:

16 units