If the sides of a square are increased by 30%, find the % increase in its area.
(a)`79%`
(b)`68%`
(c)`69%`
(d)`65%`

Options

A. `79%`
B. `68%`
C. `69%`
D. `65%`

Answer

To find the percentage increase in the area of a square when its sides are increased by 30%, we can follow these steps:

### Step 1: Understand the problem
We know that the area of a square is given by the formula:
\[ \text{Area} = \text{side}^2 \]
If the sides of the square are increased by 30%, we need to calculate the new area and then find the percentage increase from the original area.

### Step 2: Define the original side length
Let's assume the original side length of the square is \( s = 100 \) units (we can choose any value, but 100 makes calculations easier).

### Step 3: Calculate the new side length
If the side length is increased by 30%, the new side length will be:
\[ \text{New side} = s + 0.30s = 1.30s \]
Substituting \( s = 100 \):
\[ \text{New side} = 1.30 \times 100 = 130 \text{ units} \]

### Step 4: Calculate the original area
The original area of the square is:
\[ \text{Original Area} = s^2 = 100^2 = 10000 \text{ square units} \]

### Step 5: Calculate the new area
The new area of the square with the new side length is:
\[ \text{New Area} = (\text{New side})^2 = 130^2 = 16900 \text{ square units} \]

### Step 6: Calculate the increase in area
The increase in area is given by:
\[ \text{Increase in Area} = \text{New Area} - \text{Original Area} = 16900 - 10000 = 6900 \text{ square units} \]

### Step 7: Calculate the percentage increase in area
The percentage increase in area is calculated as:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Area}}{\text{Original Area}} \right) \times 100 \]
Substituting the values:
\[ \text{Percentage Increase} = \left( \frac{6900}{10000} \right) \times 100 = 69\% \]

### Final Answer
The percentage increase in the area of the square is \( 69\% \), which corresponds to option (c).

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