Divide a line segment of length 9.6 cm in the ratio 5:3 then the measure the two parts will be

Solution:

• Draw the line segment of the given length.
• Then draw another line that makes an acute angle with the given line.
• Divide the line into m + n parts where m and n are the ratios given.
• The basic proportionality theorem states that “If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally".

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, A₂ ,….A₁₃ on AX such that AA₁ = A₁A₂ = A₂A₃ =...... A₁₂A₁₃
4. Join BA₁₃
5. Through A₅ (since we need 5 parts to 8 parts) draw CA₅ parallel to BA₁₃ 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:

CA₅ is parallel to BA₁₃

By Basic Proportionality theorem, in ΔAA₁₃B

AC/BC = AA₅/A₅A₁₃ = 5/8 (By Construction)

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

☛ Check: NCERT Solutions for Class 10 Maths Chapter 11

Video Solution:

NCERT Solutions Class ₁0 Maths Chapter 11 Exercise 11.1 Question 1

Summary:

Point C divides the line segment AB of length 7.6 cm in the ratio of 5:8. By measurement, we find that AC = 2.9 cm and CB = 4.7 cm.

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