Răspuns:
AB ; AC ; BC d.p. cu 5 ; 12 ; 13 =>
AB/5 = AC/12 = BC/13 = k
AB = 5k
AC = 12k
BC = 13k
AB + AC + BC = 60
5k + 12k + 13k = 60
30k = 60
k = 2
AB = 5k = 10 cm
AC = 12k = 24 cm
BC = 13k = 26 cm
Verificam prin PITAGORA
BC² = AB² + AC²
676 = 576 + 100
676 = 676 (adevarat)
=> ΔABC = dreptunghic
AM = DM = AD/2 = 12cm/2 = 6 cm
CN = CD - ND = 12cm - 3cm = 9 cm
calculam prin PITAGORA
BM² = AB² + AM² = 12² + 6² = 144 + 36 = 180
MN² = DN² + DM² = 6² + 3² = 36 + 9 = 45
BN² = BC² + CN² = 12² + 9² = 144 + 81 = 225
verificam prin Pitagora ΔBMN
BN² = BM² + MN²
225 = 180 + 45
225 = 225 (adevarat) =>
ΔBMN = dreptunghic
