It the side of a square is increased by `25 %` then how much percent does its area get increased ?

Options

A. A)125
B. B)156.25
C. C)50
D. D)56.25

Answer

To solve the problem of how much the area of a square increases when its side is increased by 25%, we can follow these steps:

### Step 1: Understand the initial side length
Let the initial side length of the square be \( s \).

**Hint:** Choose a simple value for \( s \) to make calculations easier, such as \( s = 4 \) units.

### Step 2: Calculate the new side length
If the side is increased by 25%, the new side length \( s' \) can be calculated as:
\[ s' = s + 0.25s = 1.25s \]

**Hint:** Remember that increasing a quantity by a percentage means adding that percentage of the original quantity to itself.

### Step 3: Calculate the initial area
The area \( A \) of the square with side length \( s \) is given by:
\[ A = s^2 \]
For \( s = 4 \):
\[ A = 4^2 = 16 \text{ square units} \]

**Hint:** The area of a square is always the side length squared.

### Step 4: Calculate the new area
Now, calculate the area \( A' \) of the square with the new side length \( s' \):
\[ A' = (s')^2 = (1.25s)^2 = 1.5625s^2 \]
For \( s = 4 \):
\[ A' = 1.5625 \times 16 = 25 \text{ square units} \]

**Hint:** When squaring a product, remember to square both the coefficient and the variable.

### Step 5: Calculate the increase in area
The increase in area \( \Delta A \) is:
\[ \Delta A = A' - A = 25 - 16 = 9 \text{ square units} \]

**Hint:** The increase is simply the difference between the new area and the original area.

### Step 6: Calculate the percentage increase in area
The percentage increase in area can be calculated using the formula:
\[ \text{Percentage Increase} = \left(\frac{\Delta A}{A}\right) \times 100\% \]
Substituting the values:
\[ \text{Percentage Increase} = \left(\frac{9}{16}\right) \times 100\% = 56.25\% \]

**Hint:** To convert a fraction to a percentage, multiply by 100.

### Final Answer
The area of the square increases by **56.25%** when the side is increased by 25%.

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