Answer:
BE = 3.6 units
BD = 12.4 units
Step-by-step explanation:
From the picture attached,
Since DE║AC, ΔBDE and ΔABC will be similar.
In these similar triangles corresponding side will be in the same ratio.
[tex]\frac{BD}{AB}=\frac{BE}{BC}[/tex]
[tex]\frac{AB-AD}{AB}=\frac{BE}{BC}[/tex]
[tex]1-\frac{AD}{AB}=\frac{BE}{BC}[/tex]
1 - [tex]\frac{BE}{AB}=\frac{BE}{BC}[/tex] [Since AD = BE]
1 - [tex]\frac{BE}{16}=\frac{BE}{24}[/tex]
1 = [tex]\frac{BE}{16}+\frac{BE}{24}[/tex]
1 = [tex]BE(\frac{3+2}{48})[/tex]
BE = [tex]\frac{18}{5}[/tex]
BE = 3.6 units
Therefore, AD = BE = 3.6 units [given]
Now BD = AB - AD
= 16 - 3.6
= 12.4 units
