A man takes 6 km. distance to go around the rectangular area. If the area of the rectangle is 2 sq. km., find the difference between length and breadth.

Options

A. 2 km
B. 0.5 km
C. 1 km
D. 0.75 km

Explanation

To solve the problem step by step, we will use the information given about the perimeter and area of the rectangle.

### Step 1: Understand the given information
We know that the perimeter of the rectangle is 6 km and the area is 2 sq. km.

### Step 2: Write the formula for the perimeter
The formula for the perimeter \( P \) of a rectangle is given by:
\[ P = 2(l + b) \]
where \( l \) is the length and \( b \) is the breadth.

### Step 3: Set up the equation for the perimeter
Given that the perimeter is 6 km, we can write:
\[ 2(l + b) = 6 \]
Dividing both sides by 2:
\[ l + b = 3 \quad \text{(Equation 1)} \]

### Step 4: Write the formula for the area
The formula for the area \( A \) of a rectangle is given by:
\[ A = l \times b \]
Given that the area is 2 sq. km, we can write:
\[ l \times b = 2 \quad \text{(Equation 2)} \]

### Step 5: Express breadth in terms of length
From Equation 1, we can express \( b \) in terms of \( l \):
\[ b = 3 - l \quad \text{(Equation 3)} \]

### Step 6: Substitute Equation 3 into Equation 2
Now, substitute Equation 3 into Equation 2:
\[ l \times (3 - l) = 2 \]
Expanding this gives:
\[ 3l - l^2 = 2 \]
Rearranging it to form a quadratic equation:
\[ l^2 - 3l + 2 = 0 \]

### Step 7: Factor the quadratic equation
Now we will factor the quadratic equation:
\[ (l - 1)(l - 2) = 0 \]
This gives us two possible solutions for \( l \):
\[ l = 1 \quad \text{or} \quad l = 2 \]

### Step 8: Find the corresponding breadth for each length
1. If \( l = 1 \):
\[ b = 3 - 1 = 2 \]
2. If \( l = 2 \):
\[ b = 3 - 2 = 1 \]

### Step 9: Calculate the difference between length and breadth
Now we find the difference \( |l - b| \):
1. For \( l = 1 \) and \( b = 2 \):
\[ |1 - 2| = 1 \]
2. For \( l = 2 \) and \( b = 1 \):
\[ |2 - 1| = 1 \]

### Conclusion
In both cases, the difference between the length and breadth is:
\[ \text{Difference} = 1 \text{ km} \]