Question

PQR is a triangle, S is a point on the side QR of triangle PQR such that angle PSR equals angle QPR. Given QP equals 8 cm, P are equal 6 cm and SR equals 3 cm. Prove that triangle PQ are similar triangle a spear find the length of QR and PS find area of triangle PQ are upon area of triangleSPR

Answer 1

Answer:

Step-by-step explanation:

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)    

SP

PQ

​  

=  

PR

QR

​  

=  

SR

PR

​  

  (Properties of similar triangles)

⇒  

SP

8cm

​  

=  

3cm

6cm

​  

 

⇒SP=4cm and  

⇒  

6cm

QR

​  

=  

3cm

6cm

​  

 

⇒QR=12cm

(III)  

ar(△SPR)

ar(△PQR)

​  

=  

SP  

2

 

PQ  

2

 

​  

=  

4  

2

 

8  

2

 

​  

=4