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Calculating the perimeter of any shape involves finding the total length around the shape. For an equilateral triangle, the perimeter is straightforward to calculate. An equilateral triangle has all its sides of equal length, which simplifies the formula for perimeter calculation. If you know the length of one side, you can find the perimeter using the formula: \[ P = 3a \] where \( P \) is the perimeter, and \( a \) is the length of each side. In our problem, we are given the perimeter (96 inches), and we can use this information to find the side length. This step-by-step approach makes perimeter calculation intuitive and ensures precision.

Geometry involves various shapes and formulas, and understanding these formulas is crucial to solving geometric problems efficiently. For equilateral triangles, specific properties make some calculations straightforward, as each side is equal and each angle measures 60 degrees. The formula for the perimeter of an equilateral triangle, \[ P = 3a \], arises because of its unique property of having three equal sides. Other potential formulas for an equilateral triangle include the area formula, given by: \[ A = \frac{\sqrt{3}}{4}a^2 \], where \( A \) is the area and \( a \) again is the length of a side. Knowing these formulas allows you to quickly tackle a variety of geometry problems involving equilateral triangles.

Equations are mathematical statements that assert the equality of two expressions. Solving equations involves finding the value of an unknown variable that makes the equation true. In the case of an equilateral triangle, we used an equation to determine the side length based on the given perimeter. Given the equation: \[ 3a = 96 \] we want to find \( a \). To do this, we need to isolate \( a \) on one side of the equation, which involves dividing both sides by 3. So, \[ a = \frac{96}{3} \]. This simple division gives us the length of one side, which is 32 inches. Understanding how to rearrange and solve equations is a crucial skill in math, helping to find unknown values using given information.