In triangle ABC, DE is parallel to BC and 5 times AE equals 3 times EC. If AB = 6.4 units, find the length of DB in units.

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Given that DE is parallel to BC in triangle ABC, by the Basic Proportionality Theorem (Thales theorem), DE divides the sides proportionally.

Given 5AE = 3EC, so AE:EC = 3:5.

Since AE + EC = AC, the ratio AE:EC = 3:5 means AC is divided in the ratio 3:5.

Now, since DE || BC, the segments on AB are divided in the same ratio, so AD:DB = AE:EC = 3:5.

Given AB = 6.4 units, let AD = 3x and DB = 5x.

Then, 3x + 5x = 6.4 => 8x = 6.4 => x = 0.8.

Therefore, DB = 5x = 5 * 0.8 = 4 units.

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