Task 1228

The task

In the diagram, what is the perimeter of polygon $PQRST$? [asy] import olympiad; size(6cm); // ADJUST pair p = (0, 6); pair q = (3, 6); pair r = (3, 3); pair t = (0, 0); pair s = (7, 0); draw(p--q--r--s--t--cycle); label("$P$", p, NW); label("$Q$", q, NE); label("$R$", r, E + NE); label("$S$", s, SE); label("$T$", t, SW); label("$6$", p / 2, W); label("$3$", p + (q - p) / 2, 2 * N); label("$7$", s / 2, S); draw(rightanglemark(p, t, s)); draw(rightanglemark(t, p, q)); draw(rightanglemark(p, q, r)); add(pathticks(p--q, s=6)); add(pathticks(q--r, s=6)); [/asy]