In each of the following, give the justification of the construction also:

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

Steps of construction:

1. Draw AB = 7.6 cm
2. Draw ray AX, making an acute angle with AB
3. Mark 13 (i.e, 5 + 8) points as A₁, A_₂ ,….A_₁₃ on AX such that AA_₁ = A_₁A_₂ = A_₂A_₃ =...... A_₁₂A_₁₃
4. Join BA_₁₃
5. Through A_₅ (since we need 5 parts to 8 parts) draw CA_₅ parallel to BA_₁₃ where C lies on AB.

Now AC: CB = 5 : 8

By measurement, we find that AC = 2.9 cm and CB = 4.7 cm

Proof:

CA_₅ is parallel to BA_₁₃

By Basic Proportionality theorem, in ΔAA_₁₃B

AC/BC = AA_₅/A_₅A_₁₃ = 5/8 (By Construction)

Thus, C divides AB in the ratio 5:8.