The segment AB is divided by point C in a ratio of 4: 7, and one of the parts is 9 cm less than the other.

The segment AB is divided by point C in a ratio of 4: 7, and one of the parts is 9 cm less than the other. Find the length of each piece.

Based on the conditions of the problem, the AC segment is 4 parts, and the CB segment is 7 parts. We see that the AC segment is shorter than the CB segment by 3 parts: 7 – 4 = 3. We know that one segment is 9 cm less than the other, which means 3 parts = 9 cm.

Let’s find how many centimeters are in 1 part: 9: 3 = 3 cm.

Now we can find out the required lengths:

AC = 4 * 3 = 12 cm,

СВ = 7 * 3 = 21 cm.