A person purchases two adjacent plots, one is in rectangular shape and other is in square 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 of Rs390 (at the rate of Rs5/m). Find the side of square if the length of the rectangular plot is 15 metres.

Options

A. 10 metres
B. 12 metres
C. 8 metres
D. 9 metres

Answer

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

### Step 1: Understand the shapes and their dimensions
We have two plots: one rectangular and one square. The length of the rectangular plot is given as 15 meters, and the breadth of the rectangular plot is equal to the side of the square plot. Let's denote the breadth of the rectangular plot (and the side of the square plot) as \( B \).

**Hint:** Identify the dimensions of the plots and assign variables to unknowns.

### Step 2: Calculate the perimeter of the combined plot
The combined plot consists of the rectangular plot and the square plot. The perimeter \( P \) of the new plot can be calculated using the formula for the perimeter of a rectangle:
\[ P = 2 \times (\text{length} + \text{breadth}) \]
In our case, the length of the rectangular plot is 15 meters, and the breadth is \( B \). Therefore, the perimeter is:
\[ P = 2 \times (15 + B) \]

**Hint:** Recall the formula for the perimeter of a rectangle.

### Step 3: Set up the equation for the cost of fencing
The cost of fencing is given as Rs 390, and the rate is Rs 5 per meter. Therefore, we can express the total cost of fencing in terms of the perimeter:
\[ \text{Total Cost} = \text{Perimeter} \times \text{Cost per meter} \]
Substituting the values we have:
\[ 390 = (2 \times (15 + B)) \times 5 \]

**Hint:** Relate the total cost to the perimeter and the cost per meter.

### Step 4: Simplify the equation
First, we can divide both sides by 5 to simplify:
\[ 78 = 2 \times (15 + B) \]
Now, divide both sides by 2:
\[ 39 = 15 + B \]

**Hint:** Simplifying the equation step by step makes it easier to isolate the variable.

### Step 5: Solve for \( B \)
Now, we can solve for \( B \):
\[ B = 39 - 15 \]
\[ B = 24 \]

**Hint:** Perform basic arithmetic to find the value of the variable.

### Step 6: Find the side of the square
Since the side of the square plot is equal to the breadth of the rectangular plot, we have:
\[ \text{Side of the square} = B = 24 \text{ meters} \]

**Hint:** Remember that the side of the square is defined as equal to the breadth of the rectangular plot.

### Conclusion
The side of the square plot is **24 meters**.