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Define variables for the sides of the triangle.

Mathematics

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Answer

4x+5=304x + 5 = 30

Step-by-step solution

4 steps

  1. Define variables for the sides of the triangle.

    Let xx be the length of the shortest side in cm.
    According to the problem:
    The second side is twice as long as the shortest side, so its length is 2x2x cm.
    The third side is 5 cm longer than the shortest side, so its length is x+5x + 5 cm.

  2. Write the formula for the perimeter of a triangle.

    The perimeter PP of a triangle is the sum of its three sides.

    P=side1+side2+side3P = \text{side}_1 + \text{side}_2 + \text{side}_3

  3. Substitute the expressions for the sides and the given perimeter into the formula.

    The perimeter is given as 30 cm.

    x+2x+(x+5)=30x + 2x + (x + 5) = 30

  4. Simplify the equation.

    Combine the terms with xx:

    x+2x+x+5=30x + 2x + x + 5 = 30 4x+5=304x + 5 = 30

    This is the equation to find the length of each side.

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