Point C divides segment AB into segments AC and CB The ratio of segment AC to segment CB is 7: 3

| July 10, 2021 | education

Point C divides segment AB into segments AC and CB The ratio of segment AC to segment CB is 7: 3 Segment AC is 8cm more than segment CB WHAT IS the length of segment AB?

According to the conditions of the assignment, the ratio of the segment AC to the segment CB is 7: 3, that is, AC: CB = 7: 3. According to the main property of proportion, the following equality is true for any proportion: the product of the extreme terms of the proportion is equal to the product of the middle terms of the proportion. For our example: 3 * AC = 7 * CB.
According to another condition of the assignment, the segment AC is 8 cm larger than the segment CB, that is, AC = CB + 8 cm. Substitute this expression AC into the equality from item 1. We have 3 * (CB + 8 cm) = 7 * CB. Let’s open the brackets: 3 * CB + 3 * 8 cm = 7 * CB or 7 * CB – 3 * CB = 24 cm, whence CB = (24 cm): 4 = 6 cm.
We find AC = CB + 8 cm = 6 cm + 8 cm = 14 cm.Thus, the desired length AB = AC + CB = 14 cm + 6 cm = 20 cm.
Answers: 20 cm.



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