If the side of a square be increased by 50% What is the percent increase in area?

Options

A. 50
B. 100
C. 125
D. 150

Answer

To solve the problem of finding the percent increase in the area of a square when its side is increased by 50%, we can follow these steps:

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

### Step 2: Calculate the initial area
The area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
So, the initial area \( A_1 \) is:
\[ A_1 = x^2 \]

### Step 3: Calculate the new side length after the increase
If the side length is increased by 50%, the new side length \( x' \) can be calculated as:
\[ x' = x + 0.5x = 1.5x \]

### Step 4: Calculate the new area
Now, we can find the new area \( A_2 \) using the new side length:
\[ A_2 = (1.5x)^2 = 2.25x^2 \]

### Step 5: Find the increase in area
The increase in area \( \Delta A \) is:
\[ \Delta A = A_2 - A_1 = 2.25x^2 - x^2 = 1.25x^2 \]

### Step 6: Calculate the percent increase in area
The percent increase in area can be calculated using the formula:
\[ \text{Percent Increase} = \left( \frac{\Delta A}{A_1} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percent Increase} = \left( \frac{1.25x^2}{x^2} \right) \times 100 = 1.25 \times 100 = 125\% \]

### Final Answer
The percent increase in area when the side of the square is increased by 50% is **125%**.

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