If two adjacent sides of a square paper are decreased by 20% and 40% respectively, by what percentage does the new area decrease?

Options

A. `50%`
B. `52%`
C. `60%`
D. `48%`

Answer

To find the percentage decrease in the area of a square paper when two adjacent sides are decreased by 20% and 40%, we can follow these steps:

### Step 1: Define the original side length of the square.
Let the original side length of the square paper be \( s \).

### Step 2: Calculate the original area of the square.
The area \( A \) of a square is given by the formula:
\[ A = s^2 \]
Thus, the original area is:
\[ A_{original} = s^2 \]

### Step 3: Calculate the new lengths of the sides after the decreases.
- The first side is decreased by 20%, so the new length of this side is:
\[ s_1 = s - 0.20s = 0.80s \]
- The second side is decreased by 40%, so the new length of this side is:
\[ s_2 = s - 0.40s = 0.60s \]

### Step 4: Calculate the new area of the rectangle formed by the new side lengths.
The new area \( A_{new} \) is given by:
\[ A_{new} = s_1 \times s_2 = (0.80s) \times (0.60s) = 0.48s^2 \]

### Step 5: Calculate the decrease in area.
The decrease in area can be calculated as:
\[ \text{Decrease in area} = A_{original} - A_{new} = s^2 - 0.48s^2 = (1 - 0.48)s^2 = 0.52s^2 \]

### Step 6: Calculate the percentage decrease in area.
The percentage decrease in area is given by:
\[ \text{Percentage decrease} = \left( \frac{\text{Decrease in area}}{A_{original}} \right) \times 100 = \left( \frac{0.52s^2}{s^2} \right) \times 100 = 52\% \]

### Final Answer:
The new area decreases by **52%**.

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