Question

In AABC, point D is on AB, and point E is on BC

Answer 1

Answer:

$AC=\frac{27}{2}$

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

$\frac{BD}{AB}=\frac{DE}{AC}$ ----------(A)

Given BD=2

BA=BD+AD=2+7=9

DE=3

Putting these values in (A)

$\frac{2}{9}=\frac{3}{AC}$

$AC= \frac{3 \times 9}{2}$

$AC=\frac{27}{2}$