A man drives 4 km distance to go around a rectangular park. If the area of the rectangle is `0cdot75` sq km. Find the difference between the length and breath

Options

A. `0cdot5` km
B. 1 km
C. `2cdot75` km
D. `10cdot25` km

Answer

To solve the problem step-by-step, we need to find the difference between the length and width of a rectangular park given that the perimeter is 4 km and the area is 0.75 sq km.

### Step 1: Understand the given information
- The perimeter (P) of the rectangular park is 4 km.
- The area (A) of the rectangular park is 0.75 sq km.

### Step 2: Write the formulas for perimeter and area
The formulas for the perimeter and area of a rectangle are:
- Perimeter: \( P = 2(l + w) \)
- Area: \( A = l \times w \)

Where \( l \) is the length and \( w \) is the width.

### Step 3: Set up the equations
From the perimeter:
\[ 2(l + w) = 4 \]
Dividing both sides by 2:
\[ l + w = 2 \] (Equation 1)

From the area:
\[ l \times w = 0.75 \] (Equation 2)

### Step 4: Express one variable in terms of the other
From Equation 1, we can express \( l \) in terms of \( w \):
\[ l = 2 - w \]

### Step 5: Substitute into the area equation
Substituting \( l \) in Equation 2:
\[ (2 - w) \times w = 0.75 \]
Expanding this gives:
\[ 2w - w^2 = 0.75 \]
Rearranging it leads to:
\[ w^2 - 2w + 0.75 = 0 \]

### Step 6: Solve the quadratic equation
Now we will solve the quadratic equation using the quadratic formula:
\[ w = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]
Here, \( a = 1, b = -2, c = 0.75 \):
\[ w = \frac{-(-2) \pm \sqrt{(-2)^2 - 4 \times 1 \times 0.75}}{2 \times 1} \]
\[ w = \frac{2 \pm \sqrt{4 - 3}}{2} \]
\[ w = \frac{2 \pm \sqrt{1}}{2} \]
\[ w = \frac{2 \pm 1}{2} \]

Calculating the two possible values for \( w \):
1. \( w = \frac{3}{2} = 1.5 \)
2. \( w = \frac{1}{2} = 0.5 \)

### Step 7: Find the corresponding lengths
Using \( l = 2 - w \):
1. If \( w = 1.5 \), then \( l = 2 - 1.5 = 0.5 \)
2. If \( w = 0.5 \), then \( l = 2 - 0.5 = 1.5 \)

### Step 8: Calculate the difference between length and width
The difference \( |l - w| \) can be calculated as:
\[ |1.5 - 0.5| = 1 \]

### Final Answer
The difference between the length and width of the rectangular park is **1 km**.

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