A parallelogram and a square have the same area. If the sides of the square measure 40 m and corresponding base of the parallelogram.

Options

A. 44 m
B. 54 m
C. 64 m
D. 74 m

Answer

To solve the problem, we need to find the base of the parallelogram given that it has the same area as a square with a side length of 40 m.

### Step-by-Step Solution:

1. **Calculate the Area of the Square:**
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Given the side of the square is 40 m:
\[ A = 40 \times 40 = 1600 \, \text{m}^2 \]

2. **Set the Area of the Parallelogram Equal to the Area of the Square:**
The area of a parallelogram is given by the formula:
\[ \text{Area} = \text{base} \times \text{height} \]
Since the area of the parallelogram is equal to the area of the square, we have:
\[ \text{base} \times \text{height} = 1600 \, \text{m}^2 \]

3. **Identify the Height of the Parallelogram:**
The problem states that the height of the parallelogram is 25 m (assuming the height is given in meters, as the question does not specify units for the height).

4. **Substitute the Height into the Area Equation:**
Now we can substitute the height into the area equation:
\[ \text{base} \times 25 = 1600 \]

5. **Solve for the Base:**
To find the base, we rearrange the equation:
\[ \text{base} = \frac{1600}{25} \]
Now, calculate the base:
\[ \text{base} = 64 \, \text{m} \]

### Final Answer:
The corresponding base of the parallelogram is **64 m**.