a)
BD=4
DC=12
BC=CD+BD= 12+4=16
In ∆ABC dr =>T cat
AB² =BD×BC
AB²= 4×16
AB²=64
AB=√64
AB=8
In∆ABC dr =>T. P
AB²+AC²=BC²
8²+AC²= 16²
AC²= 256-64
AC²=192
AC=√192
AC=8√3
AD= AB×AC/BC = 88
8√3/16 =4√3
b)
DC=18
AC=30
In ∆ABC dr =>T cat
AC² =CD×BC
30²=18×BC
BC= 900:18
BC= 50
BC=CD+BD=>BD= BC-CD=50-18=32 cm
In∆ABC dr =>T. P
AB²+AC²=BC²
AB²+30²=50²
AB² =2500-900
AB²=1600
AB=√1600
AB=40
AD= AB×AC/BC =40×30/50 = 24
C)
AB=8
BC=10
In∆ABC dr =>T. P
AB²+AC²=BC²
8²+AC²=10²
AC² =100-64
AC=√36
AC=6
In ∆ABC dr =>T cat
AB² =BD×BC
8²=BD×10
64=BD×10
BD = 64:10
BD=6,4
BD=CD+BD =>CD=BC-BD=10-6,4 = 3,6
AD= AB×AC/BC =8×6/10=4,8
d)
BD=4,5
BC=18
In ∆ABC dr =>T cat
AB² =BD×BC
AB²= 4,5×18
AB² =81
AB=√81
AB= 9
In∆ABC dr =>T. P
AB²+AC²=BC
9²+AC² =18²
AC² = 324-81
AC² =243
AC= √243
AC= 9√3
BC= BD+CD=>CD= BC-BD = 18-4,5= 13,5
AD= AB×AC/BC =9×9√3/18= 9√3/2
