Question

Construct a square, if :

(i) its one side is 3.8 cm

(ii) its each side is 4.3 cm.

(iii) one diagonal is 6.2 cm.

(iv) each diagonal is 5.7 cm.

Answer 1

(i)

Steps : 1. Draw AB = 3.8 cm.

2. At B, draw $\angle \text{PBA}={90}^{\circ }$.

3. Cut BC = 3.8 cm.

4. From A and C, draw arcs of radiii 3.8 cm each which intersect at D.

5. Join AD and CD.

Thus ABCD is the required square.

(ii)

Steps :

1. Draw AB = 4.3 cm.

2. Draw $\angle \text{PAB}={90}^{\circ }$ at A.

3. Cut AD = 4.3 cm

4. From B and D, draw arcs of radii 4.3 cm each which intersect at C.

5. Join AD, BC and CD.

Hence ABCD is the required square.

(iii)

Steps : 1. Draw BD = 6.2 cm.

2. Draw perpendicular bisector XY of BD.

3. Cut OA = OC = 3.1 cm (half the diagonal)

4. Join ABCD is the required square.

(iv)

Steps :

1. Draw BD = 5.7 cm.

2. Draw perpendicular bisector XY of BD.

3. From O, draw arcs of radii equal to OB which cuts XY at A and C.

4. Join AB, AD, BC and CD.

Thus ABCD is the required square.