MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2

Question 1.
Draw a line segment of length 7.3 cm using a ruler.
Solution:
Steps of construction :
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 1
(i) Place the zero mark of the ruler at a point A.
(ii) Mark a point B at a distance of 7.3 cm from A.
(iii) Join AB.
\(\overline{A B}\) 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.
Solution:
Steps of construction :
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 2
(i) Draw a line l. Mark a point A on this line.
(ii) Place the compasses pointer on zero mark of the ruler. Open it to place the pencil point upto 5.6 cm mark.
(iii) Without changing the opening of the compasses, place the pointer on A and draw an arc that cuts l at B.
\(\overline{A B}\) is the required line segment of length 5.6 cm.

Question 3.
Construct \(\overline{A B}\) of length 7.8 cm. From this, cut off \(\overline{A C}\) of length 4.7 cm. Measure \(\overline{B C}\).
Solution:
Steps of construction :
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 3
(i) Place the zero mark of the ruler at A.
(ii) Mark a point B at a distance 7.8 cm from A.
(iii) Again, mark a point C at a distance 4.7 from A.
(iv) By measuring \(\overline{B C}\), we find that BC = 3.1 cm.

MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2

Question 4.
Given \(\overline{A B}\) of length 3.9 cm, construct \(\overline{P Q}\) such that the length of \(\overline{P Q}\) is twice that of \(\overline{A B}\). Verify by measurement.
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 4
(Hint: Construct \(\overline{P X}\) such that length of \(\overline{P X}\) = length of \(\overline{A B}\); then cut off \(\overline{X Q}\) such that \(\overline{X Q}\) also has the length of \(\overline{A B}\).)
Solution:
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 5
Steps of construction :
(i) Draw a line ‘l’.
(ii) Construct \(\overline{P X}\) such that length of \(\overline{P X}\) = length of \(\overline{A B}\) = 3.9 cm
(iii) Then cut of \(\overline{X Q}\) such that \(\overline{X Q}\) also has the length of \(\overline{A B}\).
(iv) Thus the length of \(\overline{P X}\) and the length of \(\overline{X Q}\) added together make twice the length of \(\overline{A B}\).
Verification:
By measurement we find that
PQ = 7.8 cm = 3.9 cm + 3.9 cm
= \(\overline{A B}\) + \(\overline{A B}\) = 2 × \(\overline{A B}\)

MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2

Question 5.
Given \(\overline{A B}\) of length 7.3 cm and \(\overline{C D}\) of length 3.4 cm, construct a line segment \(\overline{X Y}\) such that the length of \(\overline{X Y}\) is equal to the difference between the lengths of \(\overline{A B}\) and \(\overline{C D}\). Verify by measurement.
Solution:
Steps of construction :
(i) Draw a line ‘l’ and take a point X on it.
(ii) Construct \(\overline{X Z}\) such that length \(\overline{X Z}\) = length of \(\overline{A B}\) = 7.3 cm.
(iii) Then cut off \(\overline{Z Y}\) = length of \(\overline{C D}\) = 3.4 cm
(iv) Thus the length of \(\overline{X Y}\) = length of \(\overline{A B}\) – length of \(\overline{C D}\)
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.2 6
Verification:
By measurement, we find that length of \(\overline{X Y}\) = 3.9 cm
= 7.3 cm – 3.4 cm = \(\overline{A B}-\overline{C D}\)

MP Board Class 6th Maths Solutions

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