Final answer:
The segment AB is divided into 3 to 1 ratio by point C to find the lengths of AC and CB. Each part is calculated as 7 cm from the total length of AB (28 cm), resulting in AC being 21 cm and CB being 7 cm. The correct answer is A .
Step-by-step explanation:
The question involves finding the lengths of line segments AC and CB when a point C divides the line segment AB, which is 28 cm long, into a ratio of 3 to 1. To solve this, we can use the concept of proportionality. The sum of the ratios (3 + 1) gives us 4 parts in total. As AB is 28 cm, each part is 28 cm ÷ 4 which equals to 7 cm. Therefore, segment AC, which is 3 parts, is 3 × 7 cm = 21 cm and segment CB, which is 1 part, is 7 cm.
Summarizing:
- Total length of AB = 28 cm
- Ratio of division by point C = 3:1
- Length of each part = Total length ÷ Sum of ratios
- Length of AC = 3 × (Length of each part)
- Length of CB = 1 × (Length of each part)
Thus, the correct answer is AC = 21 cm and CB = 7 cm.
To find the lengths of line segments AC and CB, we can use the concept of ratios. Since AB is divided into the ratio 3 to 1, AC would be three-fourths (3/4) of AB and CB would be one-fourth (1/4) of AB.
Since AB = 28 cm, AC = (3/4) * 28 cm = 21 cm and CB = (1/4) * 28 cm = 7 cm.
Therefore, the correct answer is option a) AC=21 cm, CB=7 cm.