The area of a square is thrice the area of a rectangle. If the area of the square is 225 sq. cms and the length of the rectangle is 15 cms, what is the difference between the breadth of the rectangle and the side of the square ?

Options

A. 8 cms
B. 10 cms
C. 12 cms
D. 6 cms

Answer

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

### Step 1: Understand the relationship between the areas
The area of the square is given to be thrice the area of the rectangle.

### Step 2: Write down the formulas for the areas
Let:
- \( A \) = side of the square
- \( L \) = length of the rectangle
- \( B \) = breadth of the rectangle

The area of the square is:
\[ \text{Area of square} = A^2 \]

The area of the rectangle is:
\[ \text{Area of rectangle} = L \times B \]

According to the problem:
\[ A^2 = 3 \times (L \times B) \]

### Step 3: Substitute the known values
We know:
- Area of the square = 225 sq. cm
- Length of the rectangle \( L = 15 \) cm

Substituting these values into the equation:
\[ 225 = 3 \times (15 \times B) \]

### Step 4: Simplify the equation
First, simplify the right side:
\[ 225 = 3 \times 15 \times B \]
\[ 225 = 45B \]

### Step 5: Solve for \( B \)
Now, divide both sides by 45 to find \( B \):
\[ B = \frac{225}{45} \]
\[ B = 5 \text{ cm} \]

### Step 6: Find the side of the square \( A \)
We already have the area of the square:
\[ A^2 = 225 \]
To find \( A \), take the square root:
\[ A = \sqrt{225} \]
\[ A = 15 \text{ cm} \]

### Step 7: Calculate the difference between the breadth of the rectangle and the side of the square
Now we need to find the difference:
\[ \text{Difference} = A - B \]
\[ \text{Difference} = 15 - 5 \]
\[ \text{Difference} = 10 \text{ cm} \]

### Conclusion
The difference between the breadth of the rectangle and the side of the square is:
\[ \boxed{10 \text{ cm}} \]

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