Posted by **Ashley** on Monday, May 23, 2011 at 8:14pm.

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!) -
**MathMate**, Monday, May 23, 2011 at 9:12pm
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!) -
**Reiny**, Monday, May 23, 2011 at 9:13pm
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 !! -
**MathMate**, Monday, May 23, 2011 at 9:52pm
Thanks Reiny, I wasn't reading the question right!

Sorry, Ashley, please go with Reiny's answer.

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