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If ΔPQR ∼ ΔBAC, in ΔPQR, PQ = 7 cm, QR = (2x - 1) cm and in ΔABC, AB = 14 cm, AC = (3x + 1) cm, then, what is the value of QR?

  1. 7 cm
  2. 5 cm
  3. 3 cm 
  4. 9 cm

Answer (Detailed Solution Below)

Option 2 : 5 cm
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Detailed Solution

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Given:

ΔPQR ∼ ΔBAC,

In ΔPQR, PQ = 7 cm, QR = (2x - 1) cm

In ΔABC, AB = 14 cm, AC = (3x + 1) cm

Concept used:

If ΔPQR ∼ ΔBAC (Both triangle are similar)

⇒ PQ / BA = QR / AC = PR / BC

Calculation:

∴ PQ / BA = QR / AC

⇒ 7 / 14 = (2x - 1) / (3x + 1)

⇒ ½ = (2x - 1) / (3x + 1)

⇒ 3x + 1 = 4x - 2

⇒ x = 3

∴ QR = (2x - 1) = (6 - 1) = 5 cm

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-> The RRB Group D Exam Date will be announced on the official website. It is expected that the Group D Exam will be conducted in August-September 2025. 

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