+45 In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$ [asy] unitsize(1 cm); pair P, Q, R; P = (1,3); Q = (0,0); R = (4,0); draw(P--Q--R--cycle); label("$P$", P, N); label("$Q$", Q, SW); label("$R$", R, SE); label("$5$", (P + Q)/2, NW, red); label("$7$", (P + R)/2, NE, red); label("$6$", (Q + R)/2, S, red); [/asy]
+842 Since M is the midpoint of QR, then QM=MR=2QR=26=3.
Triangle PQR is a right triangle since ∠PQR=90∘ (by the Pythagorean Theorem, PQ2+QR2=PR2, so 52+62=72).
Since M is the midpoint of the hypotenuse of this right triangle, then segment PM is half the length of the hypotenuse. Therefore, PM = PR/2 = 7/2.
