Answer:
[tex]AC=\frac{27}{2}[/tex]
Step-by-step explanation:
We are given a Triangle ABC , and DE││BC , where D and E lies on AB and BC Respectively. As DE││BC , ABC is similar to BDE. Hence the ratios of the respective sides will be equal . Hence
[tex]\frac{BD}{AB}=\frac{DE}{AC}[/tex] ----------(A)
Given BD=2
BA=BD+AD=2+7=9
DE=3
Putting these values in (A)
[tex]\frac{2}{9}=\frac{3}{AC}[/tex]
[tex]AC= \frac{3 \times 9}{2}[/tex]
[tex]AC=\frac{27}{2}[/tex]
