Final answer:
To divide a line segment of 7.6 cm into a 5:8 ratio, calculate the size of one part by dividing the total length by the sum of the ratio (13 parts), then multiply the size of one part by 5 and 8 respectively to get the lengths of the two parts.
Step-by-step explanation:
To draw a line segment of 7.6 cm and divide it in the ratio 5:8, first use a ruler to measure and draw the line segment of 7.6 cm. Then, calculate the segments that are in the 5:8 ratio. We need to find out how many parts we divide 7.6 cm into by adding the ratio numbers: 5 + 8 = 13 parts in total. Now, to find the size of one part, divide the total length by the total number of parts:
7.6 cm ÷ 13 = 0.5846 cm (approximately)
Next, multiply the size of one part by each part of the ratio:
- For the '5' part: 0.5846 cm × 5 = 2.923 cm (approximately)
- For the '8' part: 0.5846 cm × 8 = 4.6768 cm (approximately)
Finally, measure and mark these lengths on the drawn line segment to get two parts measuring approximately 2.923 cm and 4.677 cm, which are in the ratio of 5:8. Note that the actual figures may slightly differ due to rounding during calculation.