Pre-algebra (DESPRATE NEED OF HELP!)

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A triangle has side lengths of (x+4), (4x-8), and (2x+8) units. If the perimeter of the triangle is at least 88 units, what is the minimum length of each side of the triangle?

  • Pre-algebra (DESPRATE NEED OF HELP!) -

    The length of each side can be calculated by the distance formula.
    For example, between (x+4) and (4x-8), the distance is:
    sqrt((4x-x)^2+(-8-4)^2)
    Sum the three sides and force the inequality of
    ∑lengths≥88.
    Solve for x.

    Note that the sides of the triangle are monotonically increasing, which means that the sum is also.

    You can solve by an iterative process. I get x(min)=13.55...
    So the lengths of each side can be calculated accordingly.

  • Pre-algebra (DESPRATE NEED OF HELP!) -

    x+4 + 4x-8 + 2x+8 ≥ 88
    7x + 4 ≥ 88
    7x ≥ 84
    x ≥ 12

    plug x = 12 into each of the side expressions

  • Pre-algebra !! -

    Thanks Reiny, I wasn't reading the question right!
    Sorry, Ashley, please go with Reiny's answer.

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