m(<A)=π-(π/4+π/6)=π-(3π+2π)/12=π-5π/12;
Din T.S⇒AB/sinC=BC/sinA ⇒6/sinπ/6=BC/sin(π-5π/12)⇒
⇒6/1/2=BC/sin5π/12⇒12=BC/(√6+√2)/4⇒
⇒12(√6+√2)=4*BC⇒BC=(12√6+12√2) cm
si:
AB/sinC=AC/sinB⇒12=AC/√2/2⇒AC*√2=12⇒AC=6√2
Deci :
P=AB+BC+AC=6√2+12√6+12√2+6=(18√2+12√6+6) cm
