Three plots having an area of 165, 195 and 285 square metres respectively are to be sub-divided into equalised flower beds.If the breadth of a bed is 3 metres, what will the maximum length of a bed ?

Options

A. 5 . 5 metres
B. 6 metres
C. 5 metres
D. 6 . 5metres

Answer

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

### Step 1: Identify the areas of the plots
The areas of the three plots are given as:
- Plot 1: 165 square meters
- Plot 2: 195 square meters
- Plot 3: 285 square meters

### Step 2: Find the HCF of the areas
To find the maximum area of equalized flower beds that can be created from these plots, we need to calculate the Highest Common Factor (HCF) of the three areas.

1. **Factors of 165**:
- 165 = 3 × 5 × 11
2. **Factors of 195**:
- 195 = 3 × 5 × 13
3. **Factors of 285**:
- 285 = 3 × 5 × 19

Now, we can identify the common factors:
- The common factors are 3 and 5.

Thus, the HCF is:
- HCF = 3 × 5 = 15

### Step 3: Calculate the maximum area of a flower bed
The maximum area of each flower bed that can be created is 15 square meters.

### Step 4: Use the breadth to find the length
We are given that the breadth (b) of each flower bed is 3 meters. To find the maximum length (l) of the flower bed, we can use the formula for area:

\[ \text{Area} = \text{Length} \times \text{Breadth} \]

Rearranging the formula to find the length gives us:

\[ \text{Length} = \frac{\text{Area}}{\text{Breadth}} = \frac{15 \text{ square meters}}{3 \text{ meters}} = 5 \text{ meters} \]

### Final Answer
The maximum length of a flower bed is **5 meters**.

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