The length and the breadth of a rectangular park are in the ratio 5:3 and its perimeter is 128m. Find the area of the park.

Options

A. `760m^2`
B. `120m^2`
C. `960m^2`
D. `64m^2`

Answer

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

### Step 1: Understand the ratio of length and breadth
The length (L) and breadth (B) of the rectangular park are in the ratio 5:3. This means we can express them in terms of a variable \(x\):
- Length \(L = 5x\)
- Breadth \(B = 3x\)

### Step 2: Use the perimeter formula
The formula for the perimeter (P) of a rectangle is given by:
\[ P = 2(L + B) \]
We know the perimeter is 128 meters, so we can set up the equation:
\[ 128 = 2(5x + 3x) \]

### Step 3: Simplify the equation
First, simplify the expression inside the parentheses:
\[ 5x + 3x = 8x \]
Now substitute this back into the equation:
\[ 128 = 2(8x) \]

### Step 4: Solve for \(x\)
Now, divide both sides of the equation by 2:
\[ 64 = 8x \]
Next, divide both sides by 8 to find \(x\):
\[ x = \frac{64}{8} = 8 \]

### Step 5: Calculate the length and breadth
Now that we have \(x\), we can find the length and breadth:
- Length \(L = 5x = 5 \times 8 = 40\) meters
- Breadth \(B = 3x = 3 \times 8 = 24\) meters

### Step 6: Calculate the area of the park
The area (A) of a rectangle is calculated using the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 40 \times 24 \]

### Step 7: Perform the multiplication
Now, calculate the area:
\[ A = 960 \text{ square meters} \]

### Final Answer
The area of the park is \(960 \, \text{m}^2\).

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