Find the area of a rectangular park which is `36(3)/(5)m` long and `16(2)/(3)`m broad.

Answer

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

### Step 1: Convert Mixed Numbers to Improper Fractions
The length of the park is given as \( 36 \frac{3}{5} \) meters. We need to convert this mixed number into an improper fraction.

- To convert \( 36 \frac{3}{5} \):
- Multiply the whole number (36) by the denominator (5): \( 36 \times 5 = 180 \)
- Add the numerator (3): \( 180 + 3 = 183 \)
- So, \( 36 \frac{3}{5} = \frac{183}{5} \) meters.

Now, let's convert the breadth \( 16 \frac{2}{3} \) meters into an improper fraction.

- To convert \( 16 \frac{2}{3} \):
- Multiply the whole number (16) by the denominator (3): \( 16 \times 3 = 48 \)
- Add the numerator (2): \( 48 + 2 = 50 \)
- So, \( 16 \frac{2}{3} = \frac{50}{3} \) meters.

### Step 2: Calculate the Area
The area \( A \) of a rectangle is calculated using the formula:
\[ A = \text{length} \times \text{breadth} \]

Substituting the values we found:
\[ A = \frac{183}{5} \times \frac{50}{3} \]

### Step 3: Multiply the Fractions
To multiply the fractions, we multiply the numerators and the denominators:
\[ A = \frac{183 \times 50}{5 \times 3} \]

Calculating the numerator:
- \( 183 \times 50 = 9150 \)

Calculating the denominator:
- \( 5 \times 3 = 15 \)

So, we have:
\[ A = \frac{9150}{15} \]

### Step 4: Simplify the Fraction
Now, we simplify \( \frac{9150}{15} \):
- Dividing both the numerator and the denominator by 15:
\[ 9150 \div 15 = 610 \]
\[ 15 \div 15 = 1 \]

Thus, the area \( A = 610 \) square meters.

### Final Answer
The area of the rectangular park is \( 610 \, \text{m}^2 \).

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