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 the QR and ST is 9 : 5. If PQ = 21.6 cm, then the length of PT is:
Answer & explanation
Correct answer: option 3
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In triangle PQR and PST
∠PQR = ∠PTS
∠P is common in both the triangle
⇒ ∠PRQ = ∠PST
Hence triangle PQR ∼ PST
Now,
\(\frac{QR}{ST}\) = \(\frac{PQ}{PT}\)
\(\frac{9}{5}\) = \(\frac{21.6}{PT}\)
PT = \(\frac{21.6 × 5}{9}\)
= 12 cm