# 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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