In ABC, DE BC and 5\,AE=3\,EC. If AB=6.4 units, then the value of DB (in units) is:

Question

In ABC, DE BC and 5\,AE=3\,EC. If AB=6.4 units, then the value of DB (in units) is:

1. A. 3.2
2. B. 5
3. C. 4 (Correct answer)
4. D. 2.4

Correct Answer

Option C — 4

Detailed Solution & Explanation

The correct answer is 4.

Key Points

• $5\,AE=3\,EC\Rightarrow\dfrac{AE}{EC}=\dfrac{3}{5}$. By the Basic Proportionality Theorem, $\dfrac{AD}{DB}=\dfrac{AE}{EC}=\dfrac{3}{5}$.
• So $\dfrac{DB}{AB}=\dfrac{5}{8}\Rightarrow DB=\dfrac{5}{8}\times6.4=4$ units.