Question

exercitiiul 13
dau 35 pcte!
va rog am nevoie sa folosesc teorema catetei ,teorema inaltimii si teorema lui pitagora

Answer 1

a)
BC=CD+BD=27+48=75 cm
In ∆ABC dr=>T. In AD² =CD×BD
AD² = 27×48
AD²=1296
AD=√1296
AD =36 cm
In∆ABC dr. T. Cat. AB²= BD ×BC
AB²= 27×75
AB² =2025
AB=√2025
AB=45 cm
In∆ABC dr =>T. P. AB² +AC²=BC²
45² +AC= 75²
AC²= 5625-2025
AC²=3600
AC=√3600
AC=60 cm

b)
In∆ABC dr=>T. Cat AC²= CD×BC
40²= 32×BC
1600= 32×BC
BC= 1600:32
BC=50 cm
BC=CD+BD=>BD= BC-CD=50-32= 18 cm
In ∆ABC dr=>T. Cat AB²=BD×BC
AB²=18×50
AB²=900
AB=√900
AB=30 cm
In∆ABC dr =>T. In AD² =CD×BD
AD²= 32×18
AD²= 576
AD=√576
AD=24 cm