[tex] \dfrac{ \dfrac{BD\cdot AD}{2} }{\dfrac{DC\cdot AD}{2}}=\dfrac49\Rightarrow\dfrac{BD}{DC}=\dfrac49\Rightarrow\dfrac{BD+DC}{DC}=\dfrac{4+9}{9}\Rightarrow\dfrac{26}{DC}=\dfrac{13}{9}\Rightarrow[/tex]
[tex]\Rightarrow DC=18\ cm\Rightarrow BD=26-18=8\ cm[/tex]
Acum, cu teorema inaltimii avem [tex]AD^2=BD\cdot DC=18\cdot8=144\Rightarrow AD=\sqrt{144}=12\ cm.[/tex]
