PQR is a triangle, right angle at Q. PN is median divide QR in equal parts ( let x)
Similarly, RM is median divide PQ in equal parts let y In △PQN, ⇒(PQ)2+(QN)2=(PN)2 ⇒(2y)2+(x)2=(9)2 ⇒4y2+x2=81 . . . (i) In △MQR, ⇒(MQ)2+(QR)2=(MR)2 ⇒(y)2+(2x)2=(7)2 ⇒y2+4x2=49 . . . (ii) In △PQR, ⇒(2y)2+(2x)2=PR2 ⇒4y2+4x2=PR2 . . . (iii) △MQN=y2+x2=9 . . . (iv) From Eq. (i) + Eq. (ii) ⇒4x2+4y2+x2+y2=130 [∴x2+y2=9] ⇒4x2+4y2=130−9 ⇒=PR2=121 PR=11cm.