NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2

These NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 Questions and Answers are prepared by our highly skilled subject experts.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.2

Question 1.
Draw a line segment of length 7.3 cm, using a ruler.
Answer:
Steps of construction:
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 1

  • Place the zero mark of the ruler at a point A.
  • Mark a point B at a distance of 7.3 cm from A.
  • Join AB.
    Hence, \(\overline{\mathrm{AB}}\) is the required line segment of length 7.3 cm.

Question 2.
Construct a line segment of length 5.6 cm using ruler and compasses.
Answer:
Steps of construction:
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 2

  • Draw a line ’l’. 1 Mark a point A on this line.
  • Place the compasses pointer on zero mark of the ruler. Open it to place the pencil point up to 5.6 cm mark.
  • Without changing the opening of the compasses. Place the pointer on A and cut an arc ’l’ at B.
    \(\overline{\mathrm{AB}}\) is the required line segment of length 5.6 cm.

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2

Question 3.
Construct \(\overline{\mathrm{AB}}\) of length 7.8 cm. From this, cut off \(\overline{\mathrm{AC}}\) of length 4.7 cm. Measure \(\overline{\mathrm{BC}}\).
Answer:
Steps of construction:
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 3

  • Place the zero mark of the ruler at A.
  • Mark a point B at a distance 7.8 cm from A.
  • Again, mark a point C at a distance 4.7 from A.
    Hence, by measuring \(\overline{\mathrm{BC}}\), we find that BC = 3.1 cm.

Question 4.
Given \(\overline{\mathrm{AB}}\) of length 3.9 cm, construct \(\overline{\mathrm{PQ}}\) such that the length of \(\overline{\mathrm{PQ}}\) is twice that of \(\overline{\mathrm{AB}}\). Verify by measurement.
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 4
(Hint: construct \(\overline{\mathrm{PX}}\) such that length of \(\overline{\mathrm{PX}}\) = length of \(\overline{\mathrm{AB}}\); then cut off \(\overline{\mathrm{XQ}}\) such that \(\overline{\mathrm{XQ}}\) also has the length of \(\overline{\mathrm{AB}}\).)
Answer:
Steps of construction:

  • Draw a line ’l’.
  • Construct \(\overline{\mathrm{PX}}\) such that length of \(\overline{\mathrm{PX}}\) = length of \(\overline{\mathrm{AB}}\)
  • Then cut of \(\overline{\mathrm{XQ}}\) such that \(\overline{\mathrm{XQ}}\) also has the length of \(\overline{\mathrm{AB}}\).
    NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 5
  • Thus the length of \(\overline{\mathrm{PX}}\) and the length of \(\overline{\mathrm{XQ}}\) added together make twice the length of \(\overline{\mathrm{AB}}\)

Verification:
Hence, by measurement we find that PQ = 7.8 cm = 3.9 cm + 3.9 cm =
\(\overline{\mathrm{AB}}+\overline{\mathrm{AB}}\) 2 × \(\overline{\mathrm{AB}}\)

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2

Question 5.
Given AB of length 7.3 cm and \(\overline{\mathrm{CD}}\) of length 3.4 cm, construct a line segment \(\overline{\mathrm{XY}}\) such that the length of \(\overline{\mathrm{XY}}\) is equal to the difference between the lengths of \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{CD}}\) Verify by measurement.
Answer:
Steps of construction:

  • Draw a line ‘l’ and take a point X on it.
  • Construct \(\overline{\mathrm{XZ}}\) such that length \(\overline{\mathrm{XZ}}\) = length of \(\overline{\mathrm{AB}}\) = 7.3 cm
  • Then cut off \(\overline{\mathrm{ZY}}\) = length of \(\overline{\mathrm{CD}}\) = 3.4 cm
  • Thus the length of \(\overline{\mathrm{XY}}\) = length of \(\overline{\mathrm{AB}}\) – length of \(\overline{\mathrm{CD}}\)
    NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.2 6
    Verification:
    Hence, by measurement we find that length of \(\overline{\mathrm{XY}}\) = 3.9 cm = 73. cm -3.4 cm = \(\overline{\mathrm{AB}}-\overline{\mathrm{CD}}\)
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