Question

In the given figure, if QR = 8 cm, QS = 5 cm and ∠PQR = 45°, then PR – PQ is equal to

• A.
  8 cm
• B.
  5 cm
• C.
  3 cm
• D.
  13 cm

Answer 1

The correct option is B

5 cm
Given: QR = 8 cm, QS = 5 cm and ∠PQR = 45°
Consider the perpendicular bisector of SR, intersecting it at point M.
∴ SM = RM and ∠PMS = ∠PMR (By construction)
Also, PM is common in both ΔPSM and ΔPRM.
⇒ ΔPSM ≅ ΔPRM (SAS congruence rule)
⇒ PS = PR
⇒ PQ + QS = PR (⸪ PS = PQ + QS)
⇒ PR – PQ = QS
⇒ PR – PQ = 5 cm (∵ QS = 5 cm)
Hence, the correct answer is option (b).