Answer:
[tex]DE = 15[/tex]
[tex]AB = 6[/tex]
Step-by-step explanation:
Given
See attachment for triangles
Required
Determine the lengths of DE and AB
To solve for DE, we make use of the following equivalent ratio
[tex]AC : BC =CE:DE[/tex]
Substitute values
[tex]8:5 = 24:DE[/tex]
Express as fraction
[tex]\frac{8}{5} = \frac{24}{DE}[/tex]
Cross Multiply
[tex]DE * 8 = 24 *5[/tex]
[tex]DE * 8 = 120[/tex]
[tex]DE = 120/8[/tex]
[tex]DE = 15[/tex]
To solve for AB, we make use of the following equivalent ratio
[tex]AB : BC =CD:DE[/tex]
Substitute values
[tex]AB : 5 = 18 : 15[/tex]
Express as fraction
[tex]\frac{AB}{5} = \frac{18}{15}[/tex]
Multiply by 5
[tex]5 * \frac{AB}{5} = \frac{18}{15}*5[/tex]
[tex]AB= \frac{18}{15}*5[/tex]
[tex]AB= \frac{18}{3}[/tex]
[tex]AB = 6[/tex]
