The area of a rectangle is thrice that of a square. The length of the rectangle is 20 cm and the breadth of the rectangle is `(3)/(2)` times that of the side of the square. The side of the square, (in cm) is

Options

A. 10
B. 20
C. 30
D. 60

Answer

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

### Step 1: Define the variables
Let the side of the square be \( x \) cm.

### Step 2: Write the area of the square
The area of the square is given by:
\[ \text{Area of the square} = x^2 \text{ cm}^2 \]

### Step 3: Write the dimensions of the rectangle
The length of the rectangle is given as 20 cm. The breadth of the rectangle is \( \frac{3}{2} \) times the side of the square, which can be expressed as:
\[ \text{Breadth of the rectangle} = \frac{3}{2}x \text{ cm} \]

### Step 4: Write the area of the rectangle
The area of the rectangle can be calculated using the formula:
\[ \text{Area of the rectangle} = \text{Length} \times \text{Breadth} = 20 \times \frac{3}{2}x \]

### Step 5: Set up the equation based on the given condition
According to the problem, the area of the rectangle is three times that of the square:
\[ 20 \times \frac{3}{2}x = 3x^2 \]

### Step 6: Simplify the equation
First, calculate the left-hand side:
\[ 20 \times \frac{3}{2}x = 30x \]
So the equation now looks like:
\[ 30x = 3x^2 \]

### Step 7: Rearrange the equation
Rearranging gives:
\[ 3x^2 - 30x = 0 \]

### Step 8: Factor the equation
Factoring out \( 3x \):
\[ 3x(x - 10) = 0 \]

### Step 9: Solve for \( x \)
Setting each factor to zero gives:
1. \( 3x = 0 \) which implies \( x = 0 \) (not valid in this context)
2. \( x - 10 = 0 \) which implies \( x = 10 \)

### Conclusion
The side of the square is:
\[ \boxed{10 \text{ cm}} \]