Each side of a rectangular field a diminished by 40%. By how much per cent is the area of the field diminished ?

Options

A. (a) `32%`
B. (b) `64%`
C. (c) `25%`
D. (d) `16%`

Answer

To solve the problem step by step, we will first define the dimensions of the rectangular field and then calculate the area before and after the dimensions are diminished by 40%.

### Step 1: Define the original dimensions of the rectangular field
Let the original length of the rectangular field be \( L \) and the original width be \( W \).

### Step 2: Calculate the original area of the rectangular field
The area \( A \) of a rectangle is given by the formula:
\[ A = L \times W \]

### Step 3: Determine the new dimensions after a 40% reduction
If each side is diminished by 40%, the new length \( L' \) and new width \( W' \) can be calculated as follows:
\[ L' = L - 0.4L = 0.6L \]
\[ W' = W - 0.4W = 0.6W \]

### Step 4: Calculate the new area of the rectangular field
The new area \( A' \) after the reduction is:
\[ A' = L' \times W' = (0.6L) \times (0.6W) = 0.36LW \]

### Step 5: Calculate the decrease in area
The decrease in area can be calculated as:
\[ \text{Decrease in Area} = A - A' = LW - 0.36LW = (1 - 0.36)LW = 0.64LW \]

### Step 6: Calculate the percentage decrease in area
To find the percentage decrease in area, we use the formula:
\[ \text{Percentage Decrease} = \left( \frac{\text{Decrease in Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values, we get:
\[ \text{Percentage Decrease} = \left( \frac{0.64LW}{LW} \right) \times 100 = 64\% \]

### Conclusion
Thus, the area of the field is diminished by **64%**.

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