The breadth of a rectangle is six times of its length. If the area of the rectangle is 864, then what is the breadth of the rectangle?

Options

A. a)21
B. b)84
C. c)72
D. d)56

Answer

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

### Step 1: Define the Variables
Let the length of the rectangle be denoted as \( l \). According to the problem, the breadth \( b \) is six times the length. Therefore, we can express the breadth as:
\[ b = 6l \]

### Step 2: Write the Area Formula
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times b \]
Substituting the expression for breadth into the area formula, we get:
\[ A = l \times (6l) = 6l^2 \]

### Step 3: Set Up the Equation
We know from the problem that the area of the rectangle is 864. Therefore, we can set up the equation:
\[ 6l^2 = 864 \]

### Step 4: Solve for \( l^2 \)
To isolate \( l^2 \), we divide both sides of the equation by 6:
\[ l^2 = \frac{864}{6} \]
Calculating the right side:
\[ l^2 = 144 \]

### Step 5: Solve for \( l \)
Next, we take the square root of both sides to find \( l \):
\[ l = \sqrt{144} = 12 \]

### Step 6: Calculate the Breadth
Now that we have the length, we can find the breadth using the expression we defined earlier:
\[ b = 6l = 6 \times 12 = 72 \]

### Conclusion
Thus, the breadth of the rectangle is:
\[ \boxed{72} \]