Răspuns:
[tex]\boldsymbol{ \red{BD = 18 \ cm}} , \boldsymbol{ \red{CD = 27 \ cm}}, \boldsymbol{ \red{AB = 9\sqrt{10} \ cm}}\\[/tex]
[tex]\boldsymbol{ \red{AC = 9\sqrt{15} \ cm}} , \boldsymbol{ \red{AD = 9\sqrt{6} \ cm}}[/tex]
Explicație pas cu pas:
ΔABC, ∡A = 90°, AD⊥BC, D∈(BC), BC = 45 cm, BD/CD = 2/3
[tex]\dfrac{BD}{CD} = \dfrac{2}{3} \Rightarrow \dfrac{BD}{BD+CD} = \dfrac{2}{2 + 3} \Rightarrow \dfrac{BD}{BC} = \dfrac{2}{5} \Rightarrow BD = \dfrac{2 \cdot 45}{5} = 18 \ cm[/tex]
CD = BC - BD = 45 - 18 = 27 cm
Teorema catetei:
[tex]AB = \sqrt{BD \cdot BC} = \sqrt{18 \cdot 45} = 9\sqrt{10} \ cm[/tex]
[tex]AC = \sqrt{CD \cdot BC} = \sqrt{27 \cdot 45} = 9\sqrt{15} \ cm[/tex]
Teorema înălțimii:
[tex]AD = \sqrt{BD \cdot CD} = \sqrt{18 \cdot 27} = 9\sqrt{6} \ cm[/tex]
