If the sides of a triangle are in the ratio of 2:3:4 and the perimeter is 27 cm, how can we find the length of each side?

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To find the lengths of each side of the triangle when the sides are in the ratio of 2:3:4 and the perimeter is 27 cm, we can follow these steps:

  1. Understand the ratio: The sides of the triangle are in the ratio 2:3:4. This means that we can represent the sides as:

    2. Sides = 2x, 3x, and 4x

  2. Set up the equation for perimeter: The perimeter of a triangle is the sum of the lengths of its sides. Thus:

    3. Perimeter = Side1 + Side2 + Side3 = 2x + 3x + 4x = 9x

  3. Use the given perimeter: We know that the perimeter is 27 cm, so we can equate and solve for x:

    4. 9x = 27

    x = 27 / 9 = 3

  4. Calculate each side: Now that we have the value of x, we can calculate the lengths of each side:
    • Side 1 = 2x = 2(3) = 6 cm
    • Side 2 = 3x = 3(3) = 9 cm
    • Side 3 = 4x = 4(3) = 12 cm

Final Result: The lengths of the sides of the triangle are 6 cm, 9 cm, and 12 cm.

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