The length of a rectagle is 4 cm and each of its diagonals measures 5 cm. Find its breadth.

Answer

To solve the problem of finding the breadth of a rectangle given its length and the length of its diagonals, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Length of the rectangle (AB) = 4 cm
- Length of each diagonal (AC and BD) = 5 cm

2. **Understand the Rectangle:**
- Let's denote the rectangle as ABCD, where:
- AB = Length
- BC = Breadth
- AC = Diagonal

3. **Apply the Pythagorean Theorem:**
- In triangle ABC, we can apply the Pythagorean theorem since it is a right triangle (angle ABC is 90 degrees).
- According to the Pythagorean theorem:
\[ AC^2 = AB^2 + BC^2 \]

4. **Substitute the Known Values:**
- Substitute the values we have:
\[ 5^2 = 4^2 + BC^2 \]
- This simplifies to:
\[ 25 = 16 + BC^2 \]

5. **Solve for BC^2:**
- Rearranging the equation gives:
\[ BC^2 = 25 - 16 \]
- Therefore:
\[ BC^2 = 9 \]

6. **Calculate BC:**
- Taking the square root of both sides:
\[ BC = \sqrt{9} = 3 \]
- Since length cannot be negative, we take the positive value:
\[ BC = 3 \text{ cm} \]

7. **Conclusion:**
- The breadth of the rectangle is 3 cm.

### Final Answer:
The breadth of the rectangle is **3 cm**.

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