On increasing each side of a square by 50%, the ratio of the area of new square formed and the given square will be

Options

A. `9:5`
B. `9:35`
C. `9:7`
D. `9:4`

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the problem
We need to find the ratio of the area of a new square formed after increasing each side of an original square by 50% to the area of the original square.

### Step 2: Define the side length of the original square
Let the side length of the original square be \( L \).

### Step 3: Calculate the area of the original square
The area \( A_1 \) of the original square is given by:
\[ A_1 = L^2 \]

### Step 4: Calculate the new side length after a 50% increase
Increasing each side by 50% means the new side length \( L' \) is:
\[ L' = L + 0.5L = 1.5L \]

### Step 5: Calculate the area of the new square
The area \( A_2 \) of the new square is:
\[ A_2 = (L')^2 = (1.5L)^2 = 2.25L^2 \]

### Step 6: Find the ratio of the areas
Now, we need to find the ratio of the area of the new square \( A_2 \) to the area of the original square \( A_1 \):
\[ \text{Ratio} = \frac{A_2}{A_1} = \frac{2.25L^2}{L^2} \]

### Step 7: Simplify the ratio
Since \( L^2 \) cancels out, we have:
\[ \text{Ratio} = 2.25 \]

### Step 8: Express the ratio in fractional form
To express \( 2.25 \) as a fraction:
\[ 2.25 = \frac{225}{100} = \frac{9}{4} \]

### Final Answer
Thus, the ratio of the area of the new square to the area of the original square is:
\[ \frac{9}{4} \]

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