Question : In ΔPQR, PS is the internal bisector of $\angle P$ meeting QR at S, PQ = 16 cm, PR = 22.4 cm, QR = 9.6 cm. The length of SR (in cm) is:
Option 1: 4
Option 2: 4.4
Option 3: 6
Option 4: 5.6
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Correct Answer: 5.6
Solution : Given, PS is the internal angle bisector of $\angle P$ We know that The angle bisector of a triangle divides the opposite sides into two segments that are proportional to the other side of the triangle ⇒ $\frac{PQ}{PR} = \frac{QS}{SR}$ ⇒ $\frac{16}{22.4} = \frac{QS}{SR}$ ⇒ $\frac{QS}{SR} = \frac{5}{7}$ It is given that QR = 9.6 cm ⇒ QS + SR = 9.6 cm ⇒ 5 unit + 7 unit = 9.6 cm ⇒ 12 unit = 9.6 cm ⇒ 1 unit = 0.8 cm ⇒ QS = (5 × 0.8) cm and SR = (7 × 0.8) cm ⇒ QS = 4 cm and SR = 5.6 cm Hence, the correct answer is 5.6 cm.
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