Answer:
Step-by-step explanation:
Let a be the length of the altitude, then from the given triangles, applying the basic proportionality theorem, we get
[tex]\frac{BD}{AD}=\frac{DC}{BD}[/tex]
⇒[tex](BD)^{2}=DC{\times}AD[/tex]
⇒[tex](BD)^2=9{\times}16[/tex]
⇒[tex]BD=\sqrt{144}[/tex]
⇒[tex]BD=12 cm[/tex]
Thus, the length of altitude is: 12 cm.
Now, [tex]\frac{AB}{AD}=\frac{AC}{AB}[/tex]
⇒[tex](AB)^{2}=220[/tex]
⇒[tex]AB= 14.83 cm[/tex]
Also, [tex]\frac{BC}{DC}\frac{AC}{BC}[/tex]
⇒[tex](BC)^{2}=400[/tex]
⇒[tex]BC=20 cm[/tex]
Thus, the lengths of the legs of this triangle are 14.83 and 20 cm.
