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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:
- Draw AB = 7.6 cm
- Draw ray AX, making an acute angle with AB
- Mark 13 (i.e, 5 + 8) points as A₁, A₂ ,….A₁₃ on AX such that AA₁ = A₁A₂ = A₂A₃ =...... A₁₂A₁₃
- Join BA₁₃
- 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.
☛ Related Questions:
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