The area of a rectangle 144 m long is the same as that of a square of side 84 m. The width of the rectangle is

Options

A. 7m
B. 14m
C. 49m
D. none of these

Answer

To find the width of the rectangle, we can follow these steps:

### Step 1: Calculate the area of the square.
The area of a square is calculated using the formula:
\[ \text{Area of square} = \text{side} \times \text{side} \]
Given that the side of the square is 84 m:
\[ \text{Area of square} = 84 \times 84 = 7056 \, \text{m}^2 \]

### Step 2: Set up the equation for the area of the rectangle.
The area of a rectangle is calculated using the formula:
\[ \text{Area of rectangle} = \text{length} \times \text{width} \]
We know the length of the rectangle is 144 m, and we need to find the width (let's denote it as \( w \)):
\[ \text{Area of rectangle} = 144 \times w \]

### Step 3: Set the area of the rectangle equal to the area of the square.
Since the area of the rectangle is equal to the area of the square, we can write:
\[ 144 \times w = 7056 \]

### Step 4: Solve for the width \( w \).
To find the width, we can rearrange the equation:
\[ w = \frac{7056}{144} \]
Now, perform the division:
\[ w = 49 \, \text{m} \]

### Conclusion
The width of the rectangle is 49 m.

---