Answer:
Option (C)
Step-by-step explanation:
In this question we will use the property " similarity of the triangles".
If DE and AC are parallel two triangles BED and BCA will be similar, corresponding sides of the triangles will be proportional.
[tex]\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}[/tex]
Option (A).
[tex]\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}[/tex]
[tex]\frac{22+12}{12}=\frac{14+26}{14}[/tex]
[tex]\frac{34}{12}=\frac{40}{14}[/tex]
[tex]\frac{17}{6}=\frac{20}{7}[/tex]
But [tex]\frac{17}{6}\neq \frac{20}{7}[/tex]
Therefore, given triangles are not similar.
AC and DE are not parallel.
Option (B).
[tex]\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}[/tex]
[tex]\frac{25}{25-7}=\frac{21+9}{21}[/tex]
[tex]\frac{25}{18}=\frac{30}{21}[/tex]
[tex]\frac{25}{18}=\frac{10}{7}[/tex]
But [tex]\frac{25}{18}\neq \frac{10}{7}[/tex]
Therefore, AC and DE are not parallel.
Option (C).
[tex]\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}[/tex]
[tex]\frac{22.5+15}{15}=\frac{40}{40-24}[/tex]
[tex]\frac{37.5}{15}=\frac{40}{16}[/tex]
2.5 = 2.5
Therefore, AC║DE.
Option (D).
[tex]\frac{\text{BA}}{\text{BD}}=\frac{\text{BC}}{\text{BE}}[/tex]
[tex]\frac{17.5+5}{17.5}=\frac{20.4+6}{20.4}[/tex]
[tex]\frac{22.5}{17.5}=\frac{26.4}{20.4}[/tex]
[tex]\frac{9}{7}=\frac{22}{17}[/tex]
But [tex]\frac{9}{7}\neq \frac{22}{17}[/tex]
Therefore, AC and DE are not parallel.
Option (C) will be the answer.
