Question

Draw a line segment of length 76 cm and divide it in the ratio 3:4. Write the measures of both the two parts.

Hint:

To divide a line segment in a given ratio, first find the common multiplier and then multiply it by the ratio values to get the lengths of the individual parts.

Answer 1

The total length of the line segment is 76 cm. It is divided in the ratio 3:4. This means that the line segment is divided into two parts such that the first part is in the ratio of 3 parts, and the second part is in the ratio of 4 parts. Let the first part be \( x_1 \) and the second part be \( x_2 \). The total length is given by: \[ x_1 + x_2 = 76 \, \text{cm}. \] Since the ratio of the parts is 3:4, we can express this as: \[ \frac{x_1}{x_2} = \frac{3}{4}. \] Now, let’s express \( x_1 \) and \( x_2 \) in terms of a common variable. Let the common multiplier be \( k \). So: \[ x_1 = 3k \quad \text{and} \quad x_2 = 4k. \] Substitute these into the total length equation: \[ 3k + 4k = 76 \quad \Rightarrow \quad 7k = 76 \quad \Rightarrow \quad k = \frac{76}{7} \approx 10.86. \] Thus, the measures of the two parts are: \[ x_1 = 3k = 3 \times 10.86 = 32.58 \, \text{cm}, \] \[ x_2 = 4k = 4 \times 10.86 = 43.44 \, \text{cm}. \]
Conclusion: The two parts of the line segment are approximately \( 32.58 \, \text{cm} \) and \( 43.44 \, \text{cm} \).