Răspuns
Explicație pas cu pas:
-aplicam T. inaltimii in ΔABC:
=> AD²=DB·DC <=> 18²=CD·12 => CD=18²/12=324/12=27 => CD=27cm.
-daca AD⊥BC => ΔABD dreptunghic in D.
aplicam T. Pitagora in ΔABD pt. AB-ipotenuza;
=> AB²=AD²+BD²=18²+12²=324+144=468 => AB=√468=√(2²·3²·13)=6√13
=> AB=6√13cm.
AB se poate afla si aplicand T. catetei in ΔABC
=> AB²=BD·BC, unde BC=BD+DC=12+27=39 => AB²=12·39=468 => AB=√468 => AB= 6√13cm.
-cateta AC o putem afla fie cu T. Pitagora in ΔABC adica
AC²=BC²-AB²=39²-(6√13)²=1521-468=1053 => AC=√1053=9√13
sau
aplicam T. catetei in ΔABC, adica
AC²=CD·BC=27·39=1053 => AC=√1053=9√13 => AC=9√13cm.
