Answer :

which has a diagonal 6 cm.

Construction:

1) Find the side - length of the square using the length of the diagonal.

2) We know that for a square of side - length ‘**a**’, the length of diagonal is ‘**a√2**’.

3) From this, we can the length of the side is i.e, ‘**3√2**’cm.

4) So, now we draw a line segment ‘**AB**’ of length ‘**3√2**’cm.

5) Draw a line perpendicular to line segment ‘**AB**’ using protractor at point ‘**B**’.

6) Now, taking point ‘**A**’ as centre draw an arc of radius ‘**6**’cm.

7) The arc intersects the line at a point, this point is ‘**C**’.

8) Join points ‘**A**’, ’**C**’ to form the line segment ‘**AC**’ and points ‘**B**’, ’**C**’ to form line segment ‘**BC**’.

9) Now draw a perpendicular to the line segment ‘**BC**’ using protractor at point ‘**C**’.

10) Now draw a perpendicular to the line segment ‘**AB**’ using protractor at point ‘**A**’.

11) These two perpendiculars intersect at a point, this point is ‘**D**’.

12) Join points ‘**C**’, ’**D**’ to form line segment ‘**CD**’ and points ‘**A**’, ’**D**’ to form the line segment ‘**AD**’.

13) Thus square ‘**ABCD**’ is formed.

__Allister__:

1) Draw a horizontal line of the length of diagonal.

2) Mark a point as ‘**A**’ and from this point draw a line of length ‘**6**’ cm at an inclination of ‘**45 ^{0}**’ with the horizontal line.

3) Now from the end of diagonal (i.e, Point ‘**C**’) draw a line of inclination of ‘**45 ^{0}**’ with the diagonal in the direction of the horizontal line.

4) Now, the horizontal line and the line drawn towards the horizontal line will intersect at a point, this point is ‘**B**’.

5) Now draw a perpendicular to the line segment ‘**BC**’ using protractor at point ‘**C**’.

6) Now draw a perpendicular to the line segment ‘**AB**’ using protractor at point ‘**A**’.

7) Join points ‘**A**’, ’**D**’ to form the line segment ‘**AD**’ and points ‘**C**’, ’**D**’ to form line segment ‘**CD**’.

8) Thus square ‘**ABCD**’ is formed.

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