Question

Divide a 10 cm line segment in the ratio 3:2.

Hint:

To divide a line segment in a given ratio, express one part in terms of the other using the ratio, and then solve the equation.

Answer 1

We are given a 10 cm line segment and are asked to divide it in the ratio 3:2. Let the two parts of the segment be \( x \) and \( y \), where \( x \) corresponds to the 3 parts and \( y \) corresponds to the 2 parts. Thus, we have the ratio: \[ \frac{x}{y} = \frac{3}{2}. \] Also, we know that: \[ x + y = 10 \, \text{cm}. \] Now, let us express \( x \) in terms of \( y \): \[ x = \frac{3}{2}y. \] Substitute \( x = \frac{3}{2}y \) into the equation \( x + y = 10 \): \[ \frac{3}{2}y + y = 10. \] Simplify: \[ \frac{5}{2}y = 10. \] Now, solve for \( y \): \[ y = \frac{10 \times 2}{5} = 4 \, \text{cm}. \] Substitute \( y = 4 \) into \( x = \frac{3}{2}y \): \[ x = \frac{3}{2} \times 4 = 6 \, \text{cm}. \] Thus, the two parts are \( x = 6 \) cm and \( y = 4 \) cm.