Question

Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.

Hint:

To divide a line segment in a given ratio, first find the total number of parts in the ratio, then multiply the total length by the respective part of the ratio to find the lengths of the individual parts.

Answer 1

To divide a line segment in a given ratio, we use the section formula or the method of construction.
Step 1: Let the total length of the line segment be \( L = 7.6 \) cm. We need to divide it in the ratio 5 : 8.
Step 2: The sum of the ratio parts is: \[ 5 + 8 = 13. \]
Step 3: Now, find the length of one part. The length of the first part is: \[ \frac{5}{13} \times 7.6 \, \text{cm} = \frac{5 \times 7.6}{13} = 2.923 \, \text{cm}. \] The length of the second part is: \[ \frac{8}{13} \times 7.6 \, \text{cm} = \frac{8 \times 7.6}{13} = 4.615 \, \text{cm}. \] Thus, the two parts are \( 2.923 \, \text{cm} \) and \( 4.615 \, \text{cm} \).
Conclusion: The two parts of the line segment are \( 2.923 \, \text{cm} \) and \( 4.615 \, \text{cm} \).