The length and the breadth of a rectangular park are 75 m and 60 m respectively. What is the ratio of the length to the breadth of the park?

Options

A. `4 : 5`
B. `5 : 4`
C. `2 : 3`
D. `3 : 2`

Answer

To find the ratio of the length to the breadth of the rectangular park, we can follow these steps:

### Step 1: Identify the length and breadth
The length of the park is given as 75 meters, and the breadth is given as 60 meters.

### Step 2: Write the ratio
The ratio of length to breadth can be written as:
\[ \text{Ratio} = \frac{\text{Length}}{\text{Breadth}} = \frac{75}{60} \]

### Step 3: Simplify the ratio
To simplify the ratio, we need to find the greatest common divisor (GCD) of 75 and 60.

- The factors of 75 are: 1, 3, 5, 15, 25, 75
- The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60

The GCD of 75 and 60 is 15.

Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{75 \div 15}{60 \div 15} = \frac{5}{4} \]

### Step 4: Write the final ratio
Thus, the ratio of the length to the breadth of the park is:
\[ 5 : 4 \]

### Final Answer
The ratio of the length to the breadth of the rectangular park is \(5 : 4\).

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