If the side of a square is increased two times then area will increase by ______________.

Options

A. Two times
B. Four times
C. Three times
D. None of these

Answer

To solve the problem, we need to determine how the area of a square changes when its side length is doubled.

**Step 1: Understand the formula for the area of a square.**
The area \( A \) of a square is given by the formula:
\[ A = \text{side}^2 \]

**Step 2: Let the original side length be \( A \).**
Let the side length of the original square be \( A \).

**Step 3: Calculate the area of the original square.**
Using the formula for the area:
\[ \text{Area of original square} = A^2 \]

**Step 4: Determine the new side length when it is increased two times.**
If the side length is increased two times, the new side length will be:
\[ \text{New side length} = 2A \]

**Step 5: Calculate the area of the new square.**
Using the new side length in the area formula:
\[ \text{Area of new square} = (2A)^2 = 4A^2 \]

**Step 6: Find the increase in area.**
To find the increase in area, we subtract the area of the original square from the area of the new square:
\[ \text{Increase in area} = \text{Area of new square} - \text{Area of original square} = 4A^2 - A^2 = 3A^2 \]

**Step 7: Determine how many times the area has increased.**
The area of the new square is \( 4A^2 \), which is 4 times the area of the original square \( A^2 \). Therefore, the area has increased by a factor of 4.

Thus, the area will increase by **4 times**.

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