# 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.
Steps of construction:

• 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.
Steps of construction:

• 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.

Question 3.
Construct $$\overline{\mathrm{AB}}$$ of length 7.8 cm. From this, cut off $$\overline{\mathrm{AC}}$$ of length 4.7 cm. Measure $$\overline{\mathrm{BC}}$$.
Steps of construction:

• 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.

(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 $$\overline{\mathrm{AB}}$$.)
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 $$\overline{\mathrm{AB}}$$.
• 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 × $$\overline{\mathrm{AB}}$$

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.
• 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 $$\overline{\mathrm{CD}}$$
Hence, by measurement we find that length of $$\overline{\mathrm{XY}}$$ = 3.9 cm = 73. cm -3.4 cm = $$\overline{\mathrm{AB}}-\overline{\mathrm{CD}}$$