In ΔPQR, ∠Q = 85° and ∠R = 65°. Points S and T are on the sides PQ and PR respectively such that ∠STR = 95° and the ratio of QR and ST is 9 : 5. If PQ is 21.6 cm, then the length of PT is :
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e 12 cm
From the figure:
∠PTS = 180 - 95 = 85°
and
∠PST = 180 - 115 = 65°
So, In △PST and △PRQ:
∠PST = ∠PRQ = 65°
∠PTS = ∠PQR = 85° and
∠P is common.
So,
△PST ≈ △PRQ
Hence,
PT/PQ = ST/RQ
⇒ PT/PQ = 5/9
⇒ PT = (5/9) × 21.6 = 12 cm