Question : A circle is inscribed in $\triangle $PQR touching the sides QR, PR and PQ at the points S, U and T, respectively. PQ = (QR + 5) cm, PQ = (PR + 2) cm. If the perimeter of $\triangle $PQR is 32 cm, then PR is equal to:
Option 1: 10 cm
Option 2: 13 cm
Option 3: 8 cm
Option 4: 11 cm
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Correct Answer: 11 cm
Solution :
⇒ PQ = (QR + 5) cm
⇒ PQ = (PR + 2) cm
From the above two equations,
⇒ PR = (QR +3) cm
The perimeter of $\triangle $PQR is 32 cm.
⇒ PQ + QR + PR = 32 cm
⇒ PQ + QR + PR = 32 cm
⇒ (QR + 5) + QR + (QR +3) = 32 cm
⇒ 3QR + 8 = 32
⇒ QR = 8 cm
The length of PR = (QR +3) = 8 + 3 = 11 cm
Hence, the correct answer is 11 cm.
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