Answer:
Segment BD = 15
Explanation:
If DE is parallel to BC, DE divides the segments AC and AB proportionally, so we can write the following equation:
[tex]\frac{BD}{18}=\frac{20}{24}[/tex]
So, solving for BD, we get:
[tex]\begin{gathered} \frac{BD}{18}\times18=\frac{20}{24}\times18 \\ BD=15 \end{gathered}[/tex]
In the same way, since EF is parallel to AB, we can write the following relationship
[tex]\frac{BF}{30}=\frac{24}{20}[/tex]
So, solving for BF, we get:
[tex]\begin{gathered} \frac{BF}{30}\times30=\frac{24}{20}\times30 \\ BF=36 \end{gathered}[/tex]
Therefore, using the theorem, we get that BD is 15 and BF is 36. Then, the answer is:
Segment BD = 15
