If the area of a square is `144 cm^(2)` and its perimeter is the same as the perimeter of an equilateral triangle, then what is the length of each side of the triangle?

Answer

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

### Step 1: Find the side length of the square
The area of a square is given by the formula:
\[ \text{Area} = \text{side} \times \text{side} = \text{side}^2 \]

Given that the area of the square is \( 144 \, \text{cm}^2 \), we can set up the equation:
\[ \text{side}^2 = 144 \]

To find the side length, we take the square root of both sides:
\[ \text{side} = \sqrt{144} = 12 \, \text{cm} \]

### Step 2: Calculate the perimeter of the square
The perimeter of a square is calculated using the formula:
\[ \text{Perimeter} = 4 \times \text{side} \]

Substituting the value of the side:
\[ \text{Perimeter} = 4 \times 12 = 48 \, \text{cm} \]

### Step 3: Set the perimeter of the square equal to the perimeter of the equilateral triangle
The perimeter of an equilateral triangle is given by:
\[ \text{Perimeter} = 3 \times \text{side of triangle} \]

Let the side length of the equilateral triangle be \( b \). Therefore, we can write:
\[ 3b = 48 \]

### Step 4: Solve for the side length of the equilateral triangle
To find \( b \), we divide both sides of the equation by 3:
\[ b = \frac{48}{3} = 16 \, \text{cm} \]

### Conclusion
The length of each side of the equilateral triangle is \( 16 \, \text{cm} \).

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