SOLUTION: A triangular room has three sides with lengths 2x-2, -2x+18 and 7x-27. What is the length of each side if its perimeter is 24 meters?

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Question 1146820: A triangular room has three sides with lengths 2x-2, -2x+18 and 7x-27. What is the length of each side if its perimeter is 24 meters?
Found 3 solutions by josgarithmetic, ikleyn, richwmiller:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
Is this system true?


If it is true, then solve this equation for x:
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.
First, solve the "perimeter" equation 


    (2x-2) + (-2x+18) + (7x-27) = 24.


    2x - 2x + 7x + (-2 +18 - 27) = 24


    7x - 11 = 24

    7x      = 24 + 11

    7x      = 35

     x      = 35/7 = 5.


Thus the side lengths are  2x-2   = 2*5-2   = 10-2   = 8;

                          -2x+18  = -2*5+18 = -10+18 = 8;

                           7x-27  = 7*5-27  = 35-27  = 8.


Thus you have an equilateral triangle.


The triangle inequalities are held by an OBVIOUS way.


Solved.

------------

The sequence of actions that @josgarithmetic proposes in his post is WRONG.

You  DO  NOT  NEED  check the triangle inequalities  BEFORE  finding the side lengths.

You need check these inequalities  AFTER  finding the triangle' side lengths.


So,  for your safety,  you better  IGNORE  the post by @josgarithmetic.



Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
a+b+c=24
2x-2+ -2x+18+ 7x-27=24
Solve for x
then 1st side a =2x-2
then 2nd side b =-2x+18
then 3rd side c =7x-27
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