A 24 cm segment AC is divided by point B in the ratio of 3: 5. Find the length of each part.

If the segment AC is divided by point B in the ratio of 3: 5, then this means that one length, for example AB, contains 3 equal parts of the length, and the segment BC contains 5 of the same parts of the length.

Let the length of one part be equal to x cm, then the segment AB is equal to 3x cm, and the segment BC is equal to 5x cm.By the condition of the problem, it is known that the sum of the lengths of the segments AB + BC is equal to (3x + 5x) cm or equal to the length of the segment AC or 24 cm. equation and solve it.

3x + 5x = 24;

8x = 24;

x = 24: 8;

x = 3 (cm) – length of one part;

3x = 3 * 3 = 9 (cm) – length AB;

5x = 3 * 5 = 15 (cm) – BC length.

Answer. 9 cm, 15 cm.