Answer:
[tex]DE=15[/tex] and [tex]AB=6[/tex]
Step-by-step explanation:
Since they are similar, the length CE is a ratio of length AC, length CD is a ratio of length AB and length DE is a ratio of length BC.
[tex]\frac{CE}{AC} =\frac{CD}{AB} =\frac{DE}{BC}[/tex]
Substituting the values,
[tex]\frac{24}{8} =\frac{18}{AB} =\frac{DE}{5}[/tex]
[tex]8[/tex]×[tex]18[/tex][tex]=24AB[/tex]
[tex]AB=\frac{144}{24}[/tex]
[tex]AB=6[/tex]
[tex]8[/tex]×[tex]DE[/tex][tex]=24[/tex]×[tex]5[/tex]
[tex]DE=\frac{120}{8}[/tex]
[tex]DE=15[/tex]
