The length of hall is (4/3) times its breadth. If the area of the hall be 300 square metres, the difference between the length and the breadth is -----

Options

A. A)15 metres
B. B)4 metres
C. C)3 metres
D. D)None of these

Answer

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

### Step 1: Define the Variables
Let the breadth of the hall be \( b \). According to the problem, the length \( l \) of the hall is given as:
\[ l = \frac{4}{3}b \]

### Step 2: Write the Area Formula
The area \( A \) of the hall is given by the formula:
\[ A = l \times b \]
Substituting the expression for length, we have:
\[ A = \left(\frac{4}{3}b\right) \times b = \frac{4}{3}b^2 \]

### Step 3: Set Up the Equation
We know the area of the hall is 300 square meters, so we can set up the equation:
\[ \frac{4}{3}b^2 = 300 \]

### Step 4: Solve for \( b^2 \)
To eliminate the fraction, multiply both sides of the equation by 3:
\[ 4b^2 = 900 \]
Now, divide both sides by 4:
\[ b^2 = 225 \]

### Step 5: Find the Value of \( b \)
Taking the square root of both sides gives:
\[ b = \sqrt{225} = 15 \text{ meters} \]

### Step 6: Calculate the Length \( l \)
Now, substitute \( b \) back into the equation for length:
\[ l = \frac{4}{3}b = \frac{4}{3} \times 15 = 20 \text{ meters} \]

### Step 7: Find the Difference Between Length and Breadth
Now, we can find the difference between the length and the breadth:
\[ \text{Difference} = l - b = 20 - 15 = 5 \text{ meters} \]

### Final Answer
The difference between the length and the breadth is **5 meters**.

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