Two rectangles ABCD and EFGH are congruent.
If the length of the rectangle ABCD is 12 m and its perimeter is 40 m, find the length and breadth of rectangle EFGH.

Answer

To solve the problem step by step, we will find the length and breadth of rectangle EFGH given that it is congruent to rectangle ABCD.

### Step-by-Step Solution:

1. **Understand the Properties of Congruent Rectangles**:
- Since rectangles ABCD and EFGH are congruent, their corresponding lengths and breadths are equal.

2. **Identify the Given Information**:
- Length of rectangle ABCD (L1) = 12 cm
- Perimeter of rectangle ABCD = 40 cm

3. **Recall the Formula for the Perimeter of a Rectangle**:
- The formula for the perimeter (P) of a rectangle is:
\[ P = 2 \times (Length + Breadth) \]
- We can rearrange this formula to find the breadth (B):
\[ P = 2 \times (L + B) \implies B = \frac{P}{2} - L \]

4. **Substitute the Known Values into the Perimeter Formula**:
- Substitute the perimeter and length into the rearranged formula:
\[ 40 = 2 \times (12 + B) \]

5. **Simplify the Equation**:
- Divide both sides by 2:
\[ 20 = 12 + B \]

6. **Solve for the Breadth (B)**:
- Subtract 12 from both sides:
\[ B = 20 - 12 = 8 \text{ cm} \]

7. **Conclusion for Rectangle ABCD**:
- Length (L1) = 12 cm
- Breadth (B1) = 8 cm

8. **Apply Congruence to Rectangle EFGH**:
- Since rectangles ABCD and EFGH are congruent:
- Length of rectangle EFGH (L2) = L1 = 12 cm
- Breadth of rectangle EFGH (B2) = B1 = 8 cm

### Final Answer:
- Length of rectangle EFGH = 12 cm
- Breadth of rectangle EFGH = 8 cm