The length of a rectangular Field is twice its breadth. If the perimeter of the field is 150 metres. Find its length and breadth.

Options

A. `60m,25m`
B. `50m,25m`
C. `50m,35m`
D. `70m,25m`

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the Variables
Let the breadth of the rectangular field be \( x \) meters. According to the problem, the length of the field is twice its breadth. Therefore, the length can be expressed as:
\[ \text{Length} = 2x \]

### Step 2: Write the Perimeter Formula
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(\text{Length} + \text{Breadth}) \]
Substituting the expressions for length and breadth:
\[ P = 2(2x + x) \]

### Step 3: Substitute the Given Perimeter
We know from the problem that the perimeter is 150 meters. Therefore, we can set up the equation:
\[ 2(2x + x) = 150 \]

### Step 4: Simplify the Equation
Now, simplify the equation:
\[ 2(3x) = 150 \]
\[ 6x = 150 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 6:
\[ x = \frac{150}{6} \]
\[ x = 25 \]

### Step 6: Find the Length
Now that we have the breadth, we can find the length:
\[ \text{Length} = 2x = 2 \times 25 = 50 \]

### Step 7: State the Final Answer
Thus, the dimensions of the rectangular field are:
- Breadth = \( 25 \) meters
- Length = \( 50 \) meters

---