The length of a rectangular park is thrice its breadth. If the perimeter of the park is 168 metres, find its dimensions.

Answer

To find the dimensions of the rectangular park, we will follow these steps:

### Step 1: Define the variables
Let the breadth of the rectangular park be \( x \) meters. According to the problem, the length of the park is thrice its breadth. Therefore, we can express the length as:
\[ \text{Length} = 3x \]

### Step 2: Write the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2 \times (\text{Length} + \text{Breadth}) \]
Substituting the expressions for length and breadth, we have:
\[ P = 2 \times (3x + x) \]

### Step 3: Substitute the known perimeter
We know that the perimeter of the park is 168 meters. Thus, we can set up the equation:
\[ 2 \times (3x + x) = 168 \]

### Step 4: Simplify the equation
Combine the terms inside the parentheses:
\[ 2 \times (4x) = 168 \]
This simplifies to:
\[ 8x = 168 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by 8:
\[ x = \frac{168}{8} \]
Calculating this gives:
\[ x = 21 \]

### Step 6: Find the dimensions
Now that we have the breadth, we can find the length. Recall that the length is \( 3x \):
\[ \text{Length} = 3 \times 21 = 63 \text{ meters} \]

### Conclusion
The dimensions of the rectangular park are:
- Breadth = 21 meters
- Length = 63 meters

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