Question

In APQR, PS is a median. If PQ = 9, PR = 40 and PS = 20.5, find QR.​

Answer 1

Step-by-step explanation:

In ΔPQR, point M is the midpoint of side QR

QM=MR=

2

1

QR

PQ

2

+PR

2

=2PM

2

+2QM

2

[by Apollonius theorem]

⇒(40)

2

+(42)

2

=2(29)

2

+2QM

2

⇒1600+1764=1682+2QM

2

⇒3364−1682=2QM

2

⇒1682=2QM

2

⇒QM

2

=841

⇒QM=29

⇒QR=2×29

⇒QR=58

Hence QR=58