The length of a plot is five times its breadth. A playground measuring 245 square metres occupies half of the total area of the plot. What is the length of the plot ?

Options

A. `35sqrt(2)` metres
B. `175 sqrt(2)` metres
C. 490 metres
D. `5sqrt(2)` metres

Answer

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

### Step 1: Define the Variables
Let the breadth of the plot be \( B \) meters. According to the problem, the length \( L \) of the plot is five times its breadth. Therefore, we can express the length as:
\[ L = 5B \]

### Step 2: Calculate the Total Area of the Plot
The area \( A \) of a rectangle is given by the formula:
\[ A = \text{Length} \times \text{Breadth} \]
Substituting the expressions for length and breadth, we get:
\[ A = L \times B = (5B) \times B = 5B^2 \]

### Step 3: Relate the Area to the Playground
According to the problem, a playground measuring 245 square meters occupies half of the total area of the plot. Therefore, we can write:
\[ \frac{1}{2} \times A = 245 \]
This implies:
\[ A = 2 \times 245 = 490 \text{ square meters} \]

### Step 4: Set Up the Equation
Now we can set the total area equal to the expression we derived earlier:
\[ 5B^2 = 490 \]

### Step 5: Solve for Breadth
To find \( B^2 \), divide both sides by 5:
\[ B^2 = \frac{490}{5} = 98 \]
Now, take the square root of both sides to find \( B \):
\[ B = \sqrt{98} = 7\sqrt{2} \text{ meters} \]

### Step 6: Calculate the Length
Now that we have the breadth, we can find the length \( L \):
\[ L = 5B = 5 \times 7\sqrt{2} = 35\sqrt{2} \text{ meters} \]

### Final Answer
Thus, the length of the plot is:
\[ \boxed{35\sqrt{2}} \text{ meters} \]