A wire is in the shape of a square of side 15 m. If it is opened and shaped as a rectangle of width 12 m, find its length.

Answer

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

### Step 1: Calculate the Perimeter of the Square
The perimeter (P) of a square can be calculated using the formula:
\[ P = 4 \times \text{side} \]
Given that the side of the square is 15 m, we can substitute this value into the formula:
\[ P = 4 \times 15 = 60 \text{ m} \]

### Step 2: Set Up the Perimeter of the Rectangle
The perimeter of a rectangle is given by the formula:
\[ P = 2 \times (\text{length} + \text{width}) \]
We know the width of the rectangle is 12 m. Let’s denote the length of the rectangle as \( L \). Therefore, the perimeter can be expressed as:
\[ P = 2 \times (L + 12) \]

### Step 3: Equate the Perimeters
Since the wire is reshaped from a square to a rectangle, the perimeters are equal:
\[ 60 = 2 \times (L + 12) \]

### Step 4: Simplify the Equation
Now, we will simplify the equation:
\[ 60 = 2L + 24 \]

### Step 5: Solve for Length \( L \)
To isolate \( L \), we first subtract 24 from both sides:
\[ 60 - 24 = 2L \]
\[ 36 = 2L \]
Now, divide both sides by 2:
\[ L = \frac{36}{2} = 18 \text{ m} \]

### Final Answer
The length of the rectangle is \( 18 \text{ m} \).

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