A square and a rectangle have the same perimeter. If the side of the square is 16 m and the length of the rectangle is 18 m. Find the breadth of the rectangle.

Options

A. 14 m
B. 15m
C. 16 m
D. 17m

Answer

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

### Step 1: Find the perimeter of the square.
The formula for the perimeter of a square is:
\[ P = 4 \times \text{side} \]
Given that the side of the square is 16 m, we can calculate the perimeter:
\[ P = 4 \times 16 = 64 \text{ m} \]

### Step 2: Set the perimeter of the rectangle equal to the perimeter of the square.
Since the square and the rectangle have the same perimeter, the perimeter of the rectangle is also 64 m.

### Step 3: Use the formula for the perimeter of the rectangle.
The formula for the perimeter of a rectangle is:
\[ P = 2L + 2B \]
Where \(L\) is the length and \(B\) is the breadth. We know:
\[ 2L + 2B = 64 \]
Given that the length \(L\) of the rectangle is 18 m, we can substitute this value into the equation:
\[ 2(18) + 2B = 64 \]

### Step 4: Simplify the equation.
Calculating \(2(18)\):
\[ 36 + 2B = 64 \]

### Step 5: Isolate \(2B\).
To isolate \(2B\), subtract 36 from both sides:
\[ 2B = 64 - 36 \]
\[ 2B = 28 \]

### Step 6: Solve for \(B\).
Now, divide both sides by 2 to find \(B\):
\[ B = \frac{28}{2} = 14 \text{ m} \]

### Conclusion:
The breadth of the rectangle is 14 meters.

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