The perimeter of rectangular field is 386 m and the difference between its two adjacent sides is 95 m. The side of a square field, having the same area as that of the rectangle, is:

Options

A. 64m
B. 84m
C. 74m
D. 82m

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We are given:
- The perimeter of a rectangular field is 386 m.
- The difference between its two adjacent sides (length and breadth) is 95 m.

### Step 2: Set up the equations
Let:
- Length of the rectangle = L
- Breadth of the rectangle = B

From the perimeter, we know:
\[ 2(L + B) = 386 \]
This simplifies to:
\[ L + B = 193 \quad \text{(Equation 1)} \]

From the difference between the sides, we have:
\[ L - B = 95 \quad \text{(Equation 2)} \]

### Step 3: Solve the equations
Now we will solve these two equations simultaneously.

Adding Equation 1 and Equation 2:
\[ (L + B) + (L - B) = 193 + 95 \]
This simplifies to:
\[ 2L = 288 \]
So, we find:
\[ L = \frac{288}{2} = 144 \text{ m} \]

Now, substitute L back into Equation 1 to find B:
\[ 144 + B = 193 \]
So,
\[ B = 193 - 144 = 49 \text{ m} \]

### Step 4: Calculate the area of the rectangle
The area \( A \) of the rectangle is given by:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 144 \times 49 \]

Calculating this:
\[ A = 7056 \text{ m}^2 \]

### Step 5: Find the side of the square having the same area
Let the side of the square be \( s \). The area of the square is given by:
\[ s^2 = A \]
Thus,
\[ s^2 = 7056 \]
Taking the square root of both sides:
\[ s = \sqrt{7056} \]

Calculating the square root:
\[ s = 84 \text{ m} \]

### Final Answer
The side of the square field having the same area as that of the rectangle is **84 m**.

---