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Question
In the figure, PQR is a straight line and PS || RT. If QS = 12cm, QR = 15cm, QT = 10cm and RT = 6cm, find PQ and PS.
Solution
In ΔPQS and ΔQTR
∠PQS = ∠TQR ...(verticall opposite angles)
∠SPQ = ∠QRT ...(alternate angles)
Therefore, ΔPQS ∼ ΔQTR
⇒ `"PQ"/"QS" = "QR"/"QT"`
⇒ `"PQ"/(12)(15)/(10)`
⇒ PQ = `(15 xx 12)/(10)`
⇒PQ = 18cm
Also,
⇒ `"QS"/"PS" = "QT"/"RT"`
⇒ `(12)/"PS" = (10)/(6)`
⇒ PS = `(6 xx 12)/(10)`
⇒ PQ = 7.2cm.
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