If each side of a square is increased by 25%, find the percentage change in its area?

Options

A. A) 65.25
B. B) 56.25
C. C) 65
D. D) 56

Answer

To find the percentage change in the area of a square when each side is increased by 25%, follow these steps:

### Step 1: Understand the initial area of the square
Let the side length of the square be \( s \). The area \( A \) of the square is given by the formula:
\[ A = s^2 \]

### Step 2: Calculate the initial area
Assuming the side length \( s = 100 \) units (for simplicity), the initial area would be:
\[ A = 100^2 = 10,000 \text{ square units} \]

### Step 3: Increase the side length by 25%
If each side of the square is increased by 25%, the new side length \( s' \) will be:
\[ s' = s + 0.25s = 1.25s \]
Substituting \( s = 100 \):
\[ s' = 1.25 \times 100 = 125 \text{ units} \]

### Step 4: Calculate the new area
Now, calculate the new area \( A' \) of the square with the new side length:
\[ A' = (s')^2 = (125)^2 = 15,625 \text{ square units} \]

### Step 5: Find the change in area
The change in area \( \Delta A \) is:
\[ \Delta A = A' - A = 15,625 - 10,000 = 5,625 \text{ square units} \]

### Step 6: Calculate the percentage change in area
To find the percentage change in area, use the formula:
\[ \text{Percentage Change} = \left( \frac{\Delta A}{A} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Change} = \left( \frac{5,625}{10,000} \right) \times 100 = 56.25\% \]

### Final Answer
The percentage change in the area of the square when each side is increased by 25% is **56.25%**.

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