To make a marriage tent, poles are planted along the perimeter of a square field at a distance of 5 metres from each other and the total number of poles used is 20. What is the area ( in sq metres) of the square field ?

Options

A. 500
B. 400
C. 900
D. None of these

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the arrangement of poles
We know that the poles are planted along the perimeter of a square field, with each pole spaced 5 meters apart. The total number of poles used is 20.

### Step 2: Determine the number of poles on each side
Since the field is square, there are 4 sides. If we denote the number of poles on one side as \( n \), then the total number of poles can be expressed as:
\[ \text{Total poles} = 4n \]
Given that the total number of poles is 20, we can set up the equation:
\[ 4n = 20 \]
Dividing both sides by 4 gives us:
\[ n = 5 \]
This means there are 5 poles on each side of the square.

### Step 3: Calculate the distance covered by the poles
Since the distance between each pole is 5 meters, we need to consider that the first pole is at the starting point of the side, and the last pole is at the end of the side. Therefore, the distance covered by the poles on one side can be calculated as follows:
- The distance between the first and last pole is \( (n - 1) \times \text{distance between poles} \).
- Thus, the distance for one side is:
\[ \text{Distance for one side} = (5 - 1) \times 5 = 4 \times 5 = 20 \text{ meters} \]

### Step 4: Calculate the total length of the square field
Since there are 4 sides to the square, the total perimeter \( P \) is:
\[ P = 4 \times \text{length of one side} \]
We already calculated that the length of one side is 20 meters, so:
\[ P = 4 \times 20 = 80 \text{ meters} \]

### Step 5: Calculate the area of the square field
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]
Since we found that the side length is 20 meters:
\[ A = 20 \times 20 = 400 \text{ square meters} \]

### Final Answer:
The area of the square field is **400 square meters**.

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