In the right-angled triangle QPR. PM is an altitude.

Given that QR = 8 cm and MQ = 3.5 cm, calculate the value of PR.

In △PQR and △MPR,

∠QPR = ∠PMR = 90°

∠PRQ = ∠PRM (Common)

∴ △PQR ~ △MPR [By AA]

Since, corresponding sides of similar triangle are proportional to each other.

$\therefore \dfrac{QR}{PR} = \dfrac{PR}{MR} \\[1em] \Rightarrow PR^2 = QR \times MR \\[1em] \Rightarrow PR^2 = 8 \times (8 - 3.5) \\[1em] \Rightarrow PR^2 = 8 \times 4.5 = 36 \\[1em] \Rightarrow PR = \sqrt{36} = 6 \text{ cm}.$

Hence, PR = 6 cm.