`squareABCD` is a parallelogram, `AB = 14 cm, BC =18 cm and AC = 16 cm`. Find the length of the other diagonal:

Options

A. 24 cm
B. 28cm
C. 36 cm
D. 32 cm

Answer

To find the length of the other diagonal in the parallelogram ABCD, we can use the property of the diagonals of a parallelogram. The diagonals of a parallelogram bisect each other, and we can apply the formula for the sum of the squares of the diagonals.

### Step-by-Step Solution:

1. **Identify the given lengths**:
- Let \( AB = 14 \, \text{cm} \)
- Let \( BC = 18 \, \text{cm} \)
- Let \( AC = 16 \, \text{cm} \)

2. **Use the formula for the diagonals of a parallelogram**:
The formula for the sum of the squares of the diagonals in a parallelogram is:
\[ AC^2 + BD^2 = 2(AB^2 + BC^2) \]
where \( AC \) and \( BD \) are the lengths of the diagonals.

3. **Calculate \( AB^2 \) and \( BC^2 \)**:
\[ AB^2 = 14^2 = 196 \]
\[ BC^2 = 18^2 = 324 \]

4. **Calculate \( 2(AB^2 + BC^2) \)**:
\[ AB^2 + BC^2 = 196 + 324 = 520 \]
\[ 2(AB^2 + BC^2) = 2 \times 520 = 1040 \]

5. **Calculate \( AC^2 \)**:
\[ AC^2 = 16^2 = 256 \]

6. **Substitute into the diagonal formula**:
\[ 256 + BD^2 = 1040 \]

7. **Solve for \( BD^2 \)**:
\[ BD^2 = 1040 - 256 = 784 \]

8. **Find \( BD \)**:
\[ BD = \sqrt{784} = 28 \, \text{cm} \]

### Conclusion:
The length of the other diagonal \( BD \) is \( 28 \, \text{cm} \).