Solution: Because BD is the bisector of ∠ABC, DE⊥AB,DF⊥BC.

Therefore, we can know that DE=DF from the properties of the angular bisector.

Then S△ABC=S△ABD+△ACD.

= 1/2 * DE * AB+ 1/2 * DF * BC

= 1/2 *DE*(AB+BC)

S△ABC=36㎝？ AB= 18㎝，BC= 12㎝

So 36 =1/2 * de * (18+12)

The solution is DE= 12/5 cm.

2.

AB=BC ∠ABD=∠CBD BD=BD ∴△ABD≌△CBD

∴∠ ADB =∠ CDB ∠ PMD =∠ PND = 90 PD = PD, so △ PMD △ PND.

∴PM=PN