A point lying on the segment AB divides it into two parts, the length of one of which is 24% of the other.

| March 15, 2021 | education

A point lying on the segment AB divides it into two parts, the length of one of which is 24% of the other. Find the length AB if the difference in the lengths of the obtained segments is 76 cm.

Let point C lie on the segment AB and divide it into two parts AC and BC.

1. Let us denote the length of the segment AC through x.

2. Determine the length of the segment BC:

0.24 * x = 0.24x.

3. Since the difference in the lengths of the obtained segments is 76 cm, then we compose and solve the equation:

x – 0.24x = 76;

0.76x = 76;

x = 76: 0.76;

x = 7600: 76;

x = 100.

4. The length of the AC segment is x = 100 cm.

5. What is the length of the BC segment?

0.24 * x = 0.24 * 100 = 24 cm.

6. What is the length of the segment AB?

AC + BC = 100 + 24 = 124 cm.

Answer: the length of the segment AB is 124 cm.



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