The length of a rectangle is 16 cm.If the length of diagonal is 20 cm, then what will be the breadth of the rectangle?

Options

A. 8 cm
B. 12 cm
C. 10 cm
D. 14 cm

Answer

To find the breadth of the rectangle given the length and the diagonal, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the diagonal in this case) is equal to the sum of the squares of the other two sides (length and breadth).

### Step-by-Step Solution:

1. **Identify the known values:**
- Length (L) = 16 cm
- Diagonal (D) = 20 cm
- Breadth (B) = ?

2. **Apply the Pythagorean theorem:**
According to the theorem:
\[ D^2 = L^2 + B^2 \]
Plugging in the known values:
\[ 20^2 = 16^2 + B^2 \]

3. **Calculate the squares:**
\[ 400 = 256 + B^2 \]

4. **Rearrange the equation to solve for B^2:**
\[ B^2 = 400 - 256 \]
\[ B^2 = 144 \]

5. **Take the square root to find B:**
\[ B = \sqrt{144} \]
\[ B = 12 \text{ cm} \]

### Conclusion:
The breadth of the rectangle is **12 cm**.