Length and breadth of a rectangular field are in the ratio 5 : 4. If the width of the field is 36 m, what is its length?

Options

A. 40 m
B. 45 m
C. 54 m
D. 50 m

Answer

To solve the problem step by step, we will follow the given information and use the properties of ratios.

### Step-by-Step Solution:

1. **Understand the Ratio**:
The length (L) and breadth (B) of the rectangular field are in the ratio of 5:4. This means:
\[ \frac{L}{B} = \frac{5}{4} \]

2. **Identify the Known Value**:
We know that the breadth (B) of the field is 36 meters. So, we can substitute this value into the equation.

3. **Set Up the Equation**:
Using the ratio, we can express the length in terms of the breadth:
\[ \frac{L}{36} = \frac{5}{4} \]

4. **Cross-Multiply**:
To solve for L, we cross-multiply:
\[ L \cdot 4 = 5 \cdot 36 \]

5. **Calculate the Right Side**:
Now, calculate \(5 \cdot 36\):
\[ 5 \cdot 36 = 180 \]
So, we have:
\[ 4L = 180 \]

6. **Solve for Length (L)**:
Now, divide both sides by 4 to find L:
\[ L = \frac{180}{4} = 45 \]

7. **Conclusion**:
The length of the rectangular field is 45 meters.

### Final Answer:
The length of the rectangular field is **45 meters**.

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