In triangle ABC, AC = 6, DB = 3, DE = 2 and AC // DE. Find the AB side.

Let us prove that triangles ABC and DBE are similar.

By condition, DE is parallel to AC, then the angle CAB = EDB as the corresponding angles at the intersection of parallel straight lines AC and DE secant AB. Angle B is common for triangles.

Then triangles ABC and DBE are similar in two angles.

The coefficient of similarity of triangles is: K = DE / AC = 2/6 = 1/3.

Then DB / AB = 1/3.

AB = 3 * DB = 3 * 3 = 9 cm.

Answer: The length of the AB side is 9 cm.

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