If a given ∆ABC, DE||BC and $$\tfrac{AD}{DB}=\tfrac{3}{5}$$​. If AC = 5.6 cm, then find AE.

Correct option is B

Given:

△ABC with DE∥BC.

Ratio $$\frac{AD}{DB} = \frac{3}{5}​.$$​​

AC=5.6 cm.

Find AE.

Concept Used:

By the Basic Proportionality Theorem (Thales' theorem), if a line is drawn parallel to one side of a triangle, it divides the other two sides in the same ratio.

Since DE∥BC, we have:

​$$\frac{AD}{DB} = \frac{AE}{EC} = \frac{3}{5}$$

​

Since AC=AE+EC, let AE=x and EC=y, so:

​$$x+y=5.6\\{x}{y} = \frac{3}{5}$$​​

Solution:

Using the proportion formula:

​$$x = \frac{3}{3+5} \times AC$$​​

​$$AE = \frac{3}{8} \times 5.6$$​​

​$$AE= \frac{16.8}{8}=2.1$$ cm

Option (B) is right.

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