If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side, then the quotient: `"Perimeter of rectangle"/"Perimeter of parallelogram"` is -

Options

A. Equal to 1
B. Greater to 1
C. Less than
D. Indefinite

Answer

To solve the problem, we need to find the quotient of the perimeter of a rectangle and the perimeter of a parallelogram, given that they have equal areas, the same base, and are situated on the same side.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Let the base of both the rectangle and the parallelogram be denoted as \( b \).
- Let the height of the rectangle be \( h_r \) and the height of the parallelogram be \( h_p \).
- The area of the rectangle \( A_r \) is given by:
\[ A_r = b \times h_r \]
- The area of the parallelogram \( A_p \) is given by:
\[ A_p = b \times h_p \]

2. **Set the Areas Equal**:
Since the areas are equal, we have:
\[ b \times h_r = b \times h_p \]
Assuming \( b \neq 0 \), we can divide both sides by \( b \):
\[ h_r = h_p \]

3. **Calculate the Perimeters**:
- The perimeter \( P_r \) of the rectangle is:
\[ P_r = 2(b + h_r) \]
- The perimeter \( P_p \) of the parallelogram is:
\[ P_p = 2(b + h_p) \]

4. **Substituting the Heights**:
Since \( h_r = h_p \), we can substitute \( h_p \) with \( h_r \) in the formula for the perimeter of the parallelogram:
\[ P_p = 2(b + h_r) \]

5. **Finding the Quotient**:
Now, we need to find the quotient of the perimeters:
\[ \frac{P_r}{P_p} = \frac{2(b + h_r)}{2(b + h_r)} = 1 \]

6. **Conclusion**:
Thus, the quotient of the perimeter of the rectangle to the perimeter of the parallelogram is:
\[ \frac{P_r}{P_p} = 1 \]

### Final Answer:
The quotient of the perimeter of the rectangle to the perimeter of the parallelogram is **1**.