Construct a rhombus ABCD , given that side AB=6 cm and one diagonal is 7 cm.

Answer

To construct a rhombus ABCD with side AB = 6 cm and one diagonal AC = 7 cm, follow these steps:

### Step-by-Step Solution:

1. **Draw the Base AB:**
- Using a ruler, draw a line segment AB of length 6 cm. Label the endpoints as A and B.

**Hint:** Ensure that you measure accurately to get the correct length.

2. **Find the Midpoint of AB:**
- To find the midpoint M of segment AB, measure 3 cm from A towards B. Mark this point as M.

**Hint:** The midpoint is essential for constructing the diagonals accurately.

3. **Draw the Diagonal AC:**
- From point M, use a compass to draw an arc with a radius of 3.5 cm (half of the diagonal AC, which is 7 cm). This arc will intersect the vertical line above and below point M. Label these intersection points as C and D.

**Hint:** The length of the diagonal is divided equally at the midpoint.

4. **Draw the Arcs for Points C and D:**
- Set the compass to 6 cm (the length of the sides of the rhombus). With the compass point on C, draw an arc. Then, with the compass point on D, draw another arc. The intersection of these arcs will give you the points C and D.

**Hint:** Make sure the compass remains at the same width while drawing arcs from both points.

5. **Label the Points:**
- Label the intersection points from the arcs as C and D.

**Hint:** Ensure that you clearly label all points to avoid confusion later.

6. **Join the Points:**
- Use a ruler to connect points A to C, B to C, B to D, and A to D. This forms the rhombus ABCD.

**Hint:** Double-check the lengths of all sides to confirm they are equal.

7. **Verify the Construction:**
- Measure each side (AB, BC, CD, AD) to ensure they are all equal to 6 cm and check that the diagonal AC measures 7 cm.

**Hint:** Verification is crucial to ensure the accuracy of your construction.

### Final Figure:
You should now have a rhombus ABCD where all sides are equal to 6 cm and the diagonal AC is 7 cm.