Question

Construct a rectangle ABCD ; if :

(i) AB = 4.5 cm and BC = 5.5 cm.

(ii) BC = 6.1 cm and CD = 6.8 cm.

(iii) AB = 5.0 cm and diagonal AC = 6.7 cm.

(iv) AD = 4.8 cm and diagonal AC = 6.4 cm.

(v) each diagonal is 6 cm and the angle between them is ${45}^{\circ }$.

(vi) each diagonal is 5.5 cm and the angle between them is ${60}^{\circ }$

Answer 1

(i)

Steps :

1. Draw BC = 5.5 cm.

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

3. Cut BA = 4.5 cm.

4. From A, draw an arc of radius 5.5 cm.

5. From C, draw an arc of radius 4.5 cm which meets first arc at D.

6. Join AD and CD.

Thus ABCD is the required rectangle.

(ii)

Steps : 1. Draw BC = 6.1 cm.

2. At C, draw $\angle \text{PCB}={90}^{\circ }$.

3. Cut CD = 6.8 cm.

4. Draw an arc of radius 6.8 cm from B.

5. From D, draw an arc of radius 6.1 cm which meets the first arc at A.

6. Join AB and AD.

Thus ABCD is the required rectangle.

(iii)

Steps :

1. Draw AB = 5 cm.

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

3. From A, draw an arc of radius 6.7 cm which meets XB at C.

4. From C, draw an arc of a radius 5 cm.

5. From A, draw an arc of radius equal to BC which meets first arc at D.

6. Join AD and CD. Thus ABCD is the required rectangle.

(iv)

Steps : 1. Draw AD = 4.8 cm.

2. At D, draw $\angle \text{XDA}={90}^{\circ }$

3. From A, draw an arc of radius 6.4 cm which meets DX at C.

4. From A, draw an arc of radius equal to DC.

5. From C, draw an arc of radius 4.8 cm which meets first arc at B.

6. Join AB and CB. Thus ABCD is the required rectangle.

(v) Steps :

1. Draw AC = 6 cm.

2. Bisect AC at O.

3. At O, draw $\angle \text{XOC}=45\circ$ and produce XO to Y.

4. Cut OB = OD = 3 cm (half the diagonal 6 cm)

5. Join AB, CB, AD and CD.

Thus ABCD is the required rectangle.

(vi)

Steps :

1. Draw AC = 5.5 cm.

2. Bisect AC at O.

3. At O, draw $\angle \text{XOC}={60}^{\circ }$ and produce XO to Y.

4. Cut OB = OA and OD = OA (half the diagonal AC).

5. Join AB, BC, AD and CD.

Thus ABCD is the required rectangle.