in ΔBAD dreptunghic ( AD⊥BC) : ∡BAD = 30° ⇒T∡30°⇒ BD = AB/2
in ΔEAD dreptunghic ( ED⊥AB) : ∡EAD = 30° ⇒T∡30°⇒ ED= AD/2
6√3 = AD/2⇒ AD=6√3 *2=12√3cm
in ΔBAD dreptunghic ⇒ TP⇒ AB² = AD² + BD²
AB= 2 BD ⇒ (2BD)² = (12√3)² + BD²⇒ 4BD² = 432 +BD²
4BD² - BD² = 432
3BD² = 432
BD² = 432:3
BD² = 144⇒ BD=√144=12⇒ BD=12 cm⇒ AB=24 cm
in Δ ABC dr : ∡B=60° si ∡ C=30°⇒T∡30°⇒ AB = BC/2
24=BC/2⇒ BC=48cm
⇒TP⇒ BC² = AB² +AC² ⇒ 2304 = 576+AC² ⇒ AC² = 2304-576
AC² =1728⇒ AC=24√3 cm
A ΔABC = AB *AC :2 = 24*24√3:2= 576√3:2=288√3 cm²
PΔABC = AB+AC+BC = 24+48+24√3 = 72+24√3 cm
