Question : In the given figure, $\mathrm{DE} \| \mathrm{BC}$. If $\mathrm{AD}=5 \mathrm{~cm}, \mathrm{DB}=10 \mathrm{~cm}$, and $\mathrm{AE}=8 \mathrm{~cm}$, then $\mathrm{AC}$ is:
Option 1: 24 cm
Option 2: 32 cm
Option 3: 8 cm
Option 4: 16 cm
Correct Answer: 24 cm
Solution :
In the given figure, DE || BC
Given: AD = 5 cm, DB = 10 cm, and AE = 8 cm
Triangles ADE and ABC are similar. Therefore, the ratio of their corresponding sides will be equal.
⇒ $\frac{AD}{AB} = \frac{AE}{AC}$
Putting the values, we get:
⇒ $\frac{5}{5 + 10} = \frac{8}{AC}$
$\therefore AC = \frac{8 \times 15}{5} = 24$
Hence, the correct answer is 24 cm.
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