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Question

PQR is a triangle. S is a point on the side QR of ΔPQR such that PSR=QPR/ Given QP=8cm, PR=6cm and SR=3cm.
(I) Prove ΔPQRΔ SPR
(II) Find the length of QR and PS
(III) areaofΔPQRareaofΔSPR.
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Solution

Given that:
QP=8cm,PR=6cm and SR=3cm
(I) In PQR and SPR
PRQ=SRP (Common angle)
QPR=PSR (Given that)
PQR=PSR (Properties of triangle )
PQRSPR (By AAA)
(II) PQSP=QRPR=PRSR (Properties of similar triangles)
8cmSP=6cm3cm
SP=4cm and
QR6cm=6cm3cm
QR=12cm
(III)ar(PQR)ar(SPR)=PQ2SP2=8242=4


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