The length and breadth of a rectangular park are in the ratio 4:3 and its perimeter is 56 m. The area of the field is

Options

A. `192 m^(2)`
B. `300 m^(2)`
C. `432 m^(2)`
D. `228 m^(2)`

Answer

To solve the problem step by step, follow these instructions:

### Step 1: Understand the ratio of length and breadth
The length (L) and breadth (B) of the rectangular park are given in the ratio of 4:3. We can express this as:
- Length (L) = 4x
- Breadth (B) = 3x
where x is a common multiplier.

**Hint:** Ratios can be expressed in terms of a variable to simplify calculations.

### Step 2: Write the formula for the perimeter of a rectangle
The perimeter (P) of a rectangle is given by the formula:
\[ P = 2(L + B) \]

**Hint:** Remember the formula for perimeter involves both length and breadth.

### Step 3: Set up the equation using the perimeter
Given that the perimeter is 56 m, we can substitute L and B into the perimeter formula:
\[ 56 = 2(4x + 3x) \]

**Hint:** Substitute the expressions for length and breadth into the perimeter formula to form an equation.

### Step 4: Simplify the equation
Now simplify the equation:
\[ 56 = 2(7x) \]
\[ 56 = 14x \]

**Hint:** Combine like terms to make the equation simpler.

### Step 5: Solve for x
To find x, divide both sides of the equation by 14:
\[ x = \frac{56}{14} \]
\[ x = 4 \]

**Hint:** Isolate the variable by performing the same operation on both sides of the equation.

### Step 6: Calculate the length and breadth
Now substitute the value of x back into the expressions for length and breadth:
- Length (L) = 4x = 4 × 4 = 16 m
- Breadth (B) = 3x = 3 × 4 = 12 m

**Hint:** Always substitute back to find the actual dimensions after finding the variable.

### Step 7: Calculate the area of the rectangular park
The area (A) of a rectangle is calculated using the formula:
\[ A = L \times B \]
Substituting the values we found:
\[ A = 16 \times 12 \]

**Hint:** Remember that area is found by multiplying length and breadth.

### Step 8: Perform the multiplication
Now calculate the area:
\[ A = 192 \, \text{m}^2 \]

**Hint:** Ensure to write the area in square meters since it is a measure of surface area.

### Final Answer
The area of the rectangular park is **192 m²**.