1. AB/AC = 2/3 AC = 3AB/2 = 1,5AB
AB² + AC² = BC² AB² + 2,25AB² = 1872 3,25AB² = 1872 AB² = 576
AB = 24cm AC = 36cm
2. AB/AC = 3/4 c/b = 3/4 c²/b² = 9/16 (c² + b²)/b² = 25/16
a²/b² = 25/16 a/b = 5/4
b·c/24 = a ( bc/24) /b = 5/4 c/24 = 5/4 c = 30cm
b = 4·30/3 = 40cm a = 5·40/4 = 50cm P = 120cm
3. AD ⊥BC AM = mediana ⇒⇒BM=MC = BC/2 = AM
ΔAMB = isoscel (AM = BM) = echilateral (mas∡AMB = 60°)
⇒BM = AB ⇒⇒ BC = 2AB = 48√3 cm
AC² = BC² - AB² ⇒⇒ AC = 72cm P = 72(√3 + 1)cm