Notam ABC triunghiul
ducem AD perpendicular pe BC
consideram
AB=10 cm
AC=17 cm
BC=21 cm
notam BD=x
DC=21-x
scriem inaltimea in functie de datele din enunt
AD²=10²-x²
AD²=17²-(21-x)²
egalam relatiile
10²-x²=17²-(21-x)²
100-x²=289-441+42x-x²
100=289-441+42x
42x=252
x=6 cm
AD=√(10²-6²)=√(100-36)=√64=8 cm
