The perimeter of an equilateral triangle is 72 centimeters. Let \( \ell \) represent the length of each side of the triangle. Which equation models the problem? \[ \frac{\ell}{3}=72 \] Solve this equation to find the length of each side of the triangle. centimeters

To determine the length of each side of an equilateral triangle with a perimeter of 72 centimeters, let's carefully set up and solve the appropriate equation. ### Understanding the Problem An **equilateral triangle** has all three sides of equal length. Let’s denote the length of each side by \( \ell \). The **perimeter** of a triangle is the sum of the lengths of all its sides. For an equilateral triangle: \[ \text{Perimeter} = \ell + \ell + \ell = 3\ell \] Given that the perimeter is **72 centimeters**, we can set up the equation: \[ 3\ell = 72 \] *Note:* The equation you provided, \(\frac{\ell}{3} = 72\), would incorrectly suggest that each side is much longer than the perimeter allows. It's essential to multiply the side length by 3 to find the perimeter, not divide. ### Solving the Equation Now, let's solve for \( \ell \): \[ 3\ell = 72 \] Divide both sides of the equation by **3** to isolate \( \ell \): \[ \ell = \frac{72}{3} = 24 \] ### Conclusion Each side of the equilateral triangle measures **24 centimeters**. \[ \boxed{24\ \text{centimeters}} \]