Question

in triangle pqr S and T are midpoints of PQ and PR given that St equal to 5 cm and PS equal to 12 cm and PR equal to 18 cm find the length of the median from vertex p​

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)    

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

Step-by-step explanation: