The length of the diagonal of a rectangle with sides 4 m and 3m would be

Options

A. 12 m
B. 7 m
C. 5 m
D. 14 m

Answer

To find the length of the diagonal of a rectangle with sides 4 m and 3 m, we can use the Pythagorean theorem. The diagonal of the rectangle forms a right triangle with the two sides of the rectangle.

### Step-by-Step Solution:

1. **Identify the sides of the rectangle**:
- Let the length (l) = 4 m
- Let the breadth (b) = 3 m

2. **Apply the Pythagorean theorem**:
- The diagonal (d) of the rectangle can be found using the formula:
\[ d = \sqrt{l^2 + b^2} \]

3. **Substitute the values into the formula**:
- Substitute l = 4 m and b = 3 m:
\[ d = \sqrt{(4)^2 + (3)^2} \]

4. **Calculate the squares**:
- Calculate \(4^2\) and \(3^2\):
\[ 4^2 = 16 \quad \text{and} \quad 3^2 = 9 \]

5. **Add the squares**:
- Add the results:
\[ d = \sqrt{16 + 9} = \sqrt{25} \]

6. **Calculate the square root**:
- Find the square root of 25:
\[ d = 5 \, \text{m} \]

### Final Answer:
The length of the diagonal of the rectangle is **5 meters**.

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