A person has purchased two adjacent plots, one is in rectangular shape and other is in square shape and combined them to make a single new plot. The breadth of the rectangular plot is equal to the side of the square plot and the cost of fencing the new plot is Rs. 470 (Rs. 5/m). Find the side of square if the length of the rectangular plot is 20 m.

Options

A. 12 m
B. 13 m
C. 13.5 m
D. 8.5 m

Explanation

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

### Step 1: Understand the given information
- We have a rectangular plot with a length of 20 m.
- The breadth of the rectangular plot is equal to the side of the square plot, which we will denote as \( y \).
- The cost of fencing the new combined plot is Rs. 470, and the cost of fencing per meter is Rs. 5.

### Step 2: Calculate the total perimeter of the new plot
To find the perimeter, we first need to determine how many meters of fencing are needed.

\[ \text{Total perimeter} = \frac{\text{Total cost}}{\text{Cost per meter}} = \frac{470}{5} = 94 \text{ m} \]

### Step 3: Express the perimeter in terms of \( y \)
The combined plot consists of the rectangular plot and the square plot. The dimensions are:
- Length of the rectangular plot = 20 m
- Breadth of the rectangular plot = \( y \) (which is also the side of the square plot)

The perimeter \( P \) of the combined plot can be expressed as:
\[ P = 2 \times (\text{Length} + \text{Breadth}) = 2 \times (20 + y) \]

### Step 4: Set up the equation
Now, we can set up the equation using the perimeter we calculated:
\[ 2 \times (20 + y) = 94 \]

### Step 5: Solve for \( y \)
First, divide both sides by 2:
\[ 20 + y = 47 \]

Next, subtract 20 from both sides:
\[ y = 47 - 20 = 27 \]

### Step 6: Conclusion
The side of the square plot is \( y = 27 \) m.