Explicație pas cu pas:
AB/AC=4/3
AB=4/3*AC
AB²+AC²=BC²
BD-CD=21⇒BD=CD+21
BC=BD+CD⇒BC=2CD+21
CD²=AC²-AD²
CD²=AC²-CD*BD
CD²=AC²-CD(CD+21)
2CD²=AC²-21CD⇒AC²=2CD²+21CD
AB²+AC²=BC²
(4/3*AC)²+2CD²+21CD=(2CD+21)²
16/9(2CD²+21CD)+2CD²+21CD=(2CD+21)²
25/9(2CD²+21CD)=(2CD+21)²⇒CD=27(cm)
BC=2*27+21=54+21=75(cm)
16/9*AC²+AC²=75²
25/9*AC²=75²
AC=√(75²*9)/25⇒AC=(75*3)/5⇒AC=45(cm)
AB=4/3*45=15*5=60(cm)
AD=(AB*AC)/BC=(60*45)/75⇒AD=36(cm)
Bafta!
