In AABC, point D is on AB, and point E is on BC
such that DE || AC. If DB = 2, DA = 7, and
DE = 3, what is the length of AC?
1) 8
29
3) 10.5
4) 13.5

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]

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In AABC, point D is on AB, and point E is on BC such that DE || AC. If DB = 2, DA = 7, and DE = 3, what is the length of AC? 1) 8 29 3) 10.5 4) 13.5

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In AABC, point D is on AB, and point E is on BC
such that DE || AC. If DB = 2, DA = 7, and
DE = 3, what is the length of AC?
1) 8
29
3) 10.5
4) 13.5