The segment AB 20.5 cm long was divided by points C and D into three parts, with AC: CD:

The segment AB 20.5 cm long was divided by points C and D into three parts, with AC: CD: DB = 0.12: 0.3: 0.08. Find the lengths of AC, CD and BD.

Since AC: CD: DB = 0.12: 0.3: 0.08, we denote the coefficient by the letter x, it turns out that AC = 0.12x, CD = 0.3x, DB = 0.08x.

Since the segment AB is equal to the sum of the segments AC, CD and DB, we get the equation:

AC + CD + DB = AB.

0.12x + 0.3x + 0.08x = 20.5.

0.5x = 20.5.

x = 20.5: 0.5.

x = 41.

Hence, AC = 0.12x = 0.12 * 41 = 4.92 (cm),

CD = 0.3x = 0.3 * 41 = 12.3 (cm),

DB = 0.08x = 0.08 * 41 = 3.28 (cm).

Let’s check: AB = 20.5.

4.92 + 12.3 + 3.28 = 20.5 (correct).