Question

In the figure, PR || SQ. If PR = 10cm, PT = 5cm, TQ = 6cm and ST = 9cm, calculate RT and SQ.

Answer 1

In ΔPRT and ΔSQT
∠PTR = ∠STQ   ...(veriically opposite angles)
∠RPT = ∠SQT   ...(alternate angles ∵ PR || SQ)
∴ ΔPRT ≅ ΔSQT

⇒ `"RT"/"PT" = "ST"/"TQ"`

⇒ `"RT"/(5) = (9)/(6)`

⇒ RT = `(5 xx 9)/(6)`
⇒ RT = 7.5cm
Also,

`"PT"/"PR" = "TQ"/"SQ"`

⇒ `(5)/(10) = (6)/"SQ"`

⇒ SQ = `(6 xx 10)/(5)`
⇒ SQ = 12cm.