In triangle ABC, `DE"||BC and (AD)/(DB) =3/((5))` . If AC = `4.8` cm .Find AE.

Answer

To solve the problem, we can use the properties of similar triangles. Since DE is parallel to BC, triangles ADE and ABC are similar. This means that the ratios of corresponding sides are equal.

Given:
- \( \frac{AD}{DB} = \frac{3}{5} \)
- \( AC = 4.8 \, \text{cm} \)

Let:
- \( AD = 3x \)
- \( DB = 5x \)

Now, we can find \( AB \):
\[ AB = AD + DB = 3x + 5x = 8x \]

Since triangles ADE and ABC are similar, we can set up the following ratio:
\[ \frac{AE}{AC} = \frac{AD}{AB} \]

Substituting the values we have:
\[ \frac{AE}{4.8} = \frac{3x}{8x} \]

The \( x \) cancels out:
\[ \frac{AE}{4.8} = \frac{3}{8} \]

Now, we can solve for \( AE \):
\[ AE = 4.8 \cdot \frac{3}{8} \]

Calculating \( AE \):
\[ AE = 4.8 \cdot 0.375 = 1.8 \, \text{cm} \]

Thus, the length of \( AE \) is \( 1.8 \, \text{cm} \).