Question

in triangle PQR,S is a point on qr such that PS=QR if the area of the triangle pqr is 56 cm square ps is 8 cm and the ratio of the area of PQSis 4:3 then find the length of the side QR.


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Answer 1

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 )

∴△PQR∼△SPR  (By AAA)

(II)   SPPQ=PRQR=SRPR  (Properties of similar triangles)

⇒SP8cm=3cm6cm

⇒SP=4cm and 

⇒6cmQR=3c