The length of a rectangle is three-fifth of the radius of a circle. The radius of the circle is equal to the side of a square whose area is `6400 m^2` . The area (in `m^2`) of the rectangle, if the breadth is 20 m is:

Options

A. 1200
B. 480
C. 960
D. 1000

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the side of the square
The area of the square is given as \(6400 \, m^2\). The area of a square is calculated as the square of its side length.

\[ \text{Area} = \text{side}^2 \]
Let the side of the square be \(s\). Therefore,

\[ s^2 = 6400 \]

Taking the square root of both sides, we find:

\[ s = \sqrt{6400} = 80 \, m \]

### Step 2: Determine the radius of the circle
According to the problem, the radius \(R\) of the circle is equal to the side of the square. Thus,

\[ R = s = 80 \, m \]

### Step 3: Calculate the length of the rectangle
The length \(L\) of the rectangle is given as three-fifths of the radius of the circle.

\[ L = \frac{3}{5} R \]

Substituting the value of \(R\):

\[ L = \frac{3}{5} \times 80 = 48 \, m \]

### Step 4: Find the area of the rectangle
The area \(A\) of the rectangle can be calculated using the formula:

\[ A = L \times B \]

where \(B\) is the breadth of the rectangle. Given that the breadth \(B\) is \(20 \, m\):

\[ A = 48 \times 20 = 960 \, m^2 \]

### Final Answer
The area of the rectangle is \(960 \, m^2\).

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