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.

Answer 1

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.