Following are the steps of construction of a `Delta ABC` in which AB = 6 cm, `angleA = 45^(@) and AC - BC = 4 cm`. Arrange them and select the CORRECT option.
(i) Draw AB = 6 cm
(ii) Join BC to obtain the required triangle ABC
(iii)Draw `angleBAX = 60^(@)`
(iv) From ray AX, cut offline segment AD = AC - BC = 4 cm
(V) Join BD
(vi) Draw the perpendicular bisector of BD which cuts AX at C.

Options

A. `(i) rarr (iii) rarr (iv) rarr (v) rarr (vi) rarr (ii)`
B. `(iii) rarr (i) rarr (vi) rarr (iv) rarr (ii) rarr (v)`
C. `(iii) rarr (i) rarr (ii) rarr (v) rarr (iv) rarr (vi)`
D. `(iii) rarr (ii) rarr (iv) rarr (i) rarr (vi) rarr (v)`

Answer

To construct triangle ABC with the given conditions (AB = 6 cm, ∠A = 45°, and AC - BC = 4 cm), follow these steps in the correct order:

### Step-by-Step Solution:

1. **Draw AB = 6 cm**:
- Use a ruler to draw a line segment AB that measures exactly 6 cm.

2. **Draw ∠BAX = 45°**:
- At point A, use a protractor to measure and draw an angle of 45° from line AB. Extend this line to create ray AX.

3. **Cut off segment AD = AC - BC = 4 cm**:
- From ray AX, use a compass to measure a length of 4 cm. Mark this point as D on ray AX.

4. **Join BD**:
- Use a ruler to draw a line segment from point B to point D.

5. **Draw the perpendicular bisector of BD**:
- To find the midpoint of BD, use a compass to draw arcs above and below the line segment BD from points B and D. The intersection points of these arcs will help you draw the perpendicular bisector.

6. **Label the intersection of the perpendicular bisector with ray AX as point C**:
- The point where the perpendicular bisector intersects ray AX is point C.

7. **Join BC**:
- Finally, draw a line segment from point B to point C to complete triangle ABC.

### Final Arrangement of Steps:
- (i) Draw AB = 6 cm
- (iii) Draw ∠BAX = 45°
- (iv) From ray AX, cut off segment AD = 4 cm
- (v) Join BD
- (vi) Draw the perpendicular bisector of BD which cuts AX at C
- (ii) Join BC to obtain the required triangle ABC