A triangle has sides in the ratio 3:4:5. If the perimeter of the triangle is 60 cm, what is the length of the longest side?

["Understanding the 3:4:5 Triangle Ratio: Calculating the Longest Side When Perimeter Is 60 cm", "A triangle with side lengths in the ratio 3:4:5 is one of the most famous examples of a Pythagorean triple, representing a right-angled triangle where the sides satisfy the Pythagorean theorem: (3^2 + 4^2 = 5^2). This elegant mathematical property makes it not only a staple in geometry but also a common topic in homework, quizzes, and math education.", "When dealing with such a triangle, knowing the perimeter helps determine the precise length of each side. Specifically, if the perimeter of a 3:4:5 triangle is 60 cm, we can calculate the length of the longest side—the hypotenuse—by applying the side ratios systematically.", "### Breaking Down the 3:4:5 Ratio", "In the 3:4:5 ratio, the three sides can be expressed in terms of a common multiplier (x) as follows:\n- Shortest side = (3x)\n- Middle side = (4x)\n- Longest side = (5x)", "The perimeter of the triangle is the sum of all three sides:\n[\n3x + 4x + 5x = 12x\n]", "We are told the perimeter is 60 cm:\n[\n12x = 60\n]", "Solving for (x):\n[\nx = \frac{60}{12} = 5\n]", "### Calculating the Longest Side", "Now that we know (x = 5), we compute the length of the longest side:\n[\n5x = 5 \ imes 5 = 25 \ ext{ cm}\n]", "### Conclusion", "For a triangle with sides in the ratio 3:4:5 and a perimeter of 60 cm, the longest side—the hypotenuse—is 25 cm long. This method applies any time you encounter scaled right triangles and a known perimeter, making the 3:4:5 ratio a reliable tool in geometry and real-world applications like construction, design, and navigation.", "This simple yet powerful ratio remains a cornerstone in teaching and understanding triangle proportions, proving that even basic proportions hold immense mathematical value."]