AD/BD=√3 ⇒AD=√3 ×BD ⇒AD² = 3BD²
AD²= BD×DC (teorema inaltimii)
AD²= 3BD²
⇒BD × DC = 3 BD²
⇒DC = 3BD
BC = BD +DC = BD + 3BD = 4BD
AC²= BC×DC (teorema catetei)
432 = BC ×DC
↓
432 = 4BD ×DC
dar BD ×DC = 3BD²
⇒432 = 4 ×3 ×BD²
⇒BD²= 36
BD = 6
DC= 3BD
⇒DC = 3×6 = 18
BC =BD +DC = 24
AB²= BC²-AC²
AB²= 576-432
AB²= 144
AB= 12
A= AB ×AC /2 = 12 ×12√3 / 2 = 72√3
P= AB + BC + AC = 12 + 24 + 12√3 = 36 +12√3= 12(3 +√3)
