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Question
The sides PQ and PR of the ΔPQR are produced to S and T respectively. ST is drawn parallel to QR and PQ: PS = 3:4. If PT = 9.6 cm, find PR. If 'p' be the length of the perpendicular from P to QR, find the length of the perpendicular from P to ST in terms of 'p'.
Solution
Since QR is parallel to ST
By Basic Theorem of Proportionality,
`"PQ"/"PS" = "PR"/"PT"`
⇒ `(3)/(4) = "PR"/(9.6)`
⇒ PR = `(9.6 xx 3)/(4)` = 7.2cm
Since QR is parallel to ST,
QM || SD
By Basic Theorem of Proportionality,
`"PQ"/"PS" = "PM"/"PD"`
⇒ `(3)/(4) = "P"/"PD"`
⇒ PD = `(4"p")/(3)`
So, the length of the perpendicular from P and ST in terms of p is `(4"p")/(3)`.
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