Question

c) In the given figure, PQ and TR are parallel to each other.
Sides PS and QR are 4 cm each and are perpendicular
to PQ : given that angle PTS = 60° and angle PRS = 45°
calculate: (I) PQ (ii) PR (iii) PT​

Answer 1

Answer:

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=3cm6cm

⇒QR=12cm

(III)ar(△SPR)ar(△PQR)=SP2PQ2=4282=4

Answer verified by Toppr

18042 Views

Upvote (30)

Was this answer helpful?