The length of a reactangular board is 4 times tht of its breadth. If the area of the board is 256 sq. meters, find its length.

Options

A. 8m
B. 16 m
C. 24 m
D. 32 m

Answer

To solve the problem step by step, we need to find the length of a rectangular board given that its length is 4 times its breadth and the area is 256 square meters.

### Step 1: Define the variables
Let the breadth of the rectangular board be denoted as \( b \). According to the problem, the length \( l \) is 4 times the breadth. Therefore, we can express the length as:
\[ l = 4b \]

**Hint:** Define the variables clearly to understand the relationship between length and breadth.

### Step 2: Write the formula for the area of a rectangle
The area \( A \) of a rectangle is given by the formula:
\[ A = l \times b \]
Substituting the expression for length, we have:
\[ A = (4b) \times b \]

**Hint:** Remember the formula for the area of a rectangle, which involves both length and breadth.

### Step 3: Set up the equation using the area
Given that the area of the board is 256 square meters, we can set up the equation:
\[ 4b \times b = 256 \]
This simplifies to:
\[ 4b^2 = 256 \]

**Hint:** Substitute the known area into the equation to find the relationship between breadth and area.

### Step 4: Solve for \( b^2 \)
To isolate \( b^2 \), divide both sides of the equation by 4:
\[ b^2 = \frac{256}{4} \]
\[ b^2 = 64 \]

**Hint:** Perform algebraic operations carefully to simplify the equation.

### Step 5: Find the value of \( b \)
Now, take the square root of both sides to find \( b \):
\[ b = \sqrt{64} \]
\[ b = 8 \text{ meters} \]

**Hint:** Remember that the square root gives you the positive value since length cannot be negative.

### Step 6: Calculate the length \( l \)
Now that we have the breadth, we can find the length using the relationship established earlier:
\[ l = 4b \]
Substituting the value of \( b \):
\[ l = 4 \times 8 \]
\[ l = 32 \text{ meters} \]

**Hint:** Use the relationship between length and breadth to find the final answer.

### Final Answer
The length of the rectangular board is **32 meters**.