Question

solve this question by given photo

Answer 1

In ΔPMR ,
     MQ=QR=a
∴Q is midpoint of segment MR.
∴PQ is median on side MR.
∴By Appollonius Theorem,
   PM²+PR²= 2(PQ)²+2(MQ)²
∴PM²+(a)²= 2(a)²+2(a)²
∴PM²+a²= 2a²+2a²
∴PM²=4a²-a²
∴PM²=3a²
∴PM=√3a

Similarly, by taking PR as median in ΔPQR, we can prove PN²=√3a

∴PM=PN=√3a