SOLUTION: Please, I need help with the following problem regarding shapes and their sizes. Also please show your work if possible so that I can understand the answer: A regular hexagon, a s

Question 892754: Please, I need help with the following problem regarding shapes and their sizes. Also please show your work if possible so that I can understand the answer:
A regular hexagon, a square, and an equilateral triangle all have equal sides. If the sum of the perimeters of the square and the triangle is no more than 18 cm less than twice the perimeter of the hexagon, what is the minimum length of each side?
Answer by LinnW(1048) (Show Source): You can put this solution on YOUR website!
Let x = the length of a side
triangle perimeter = 3x
square perimeter = 4x
hexagon perimeter = 6x
sum of perimeters of the square and the triangle is 3x + 4x
*****************
Below states that sum of perimeters of square and triangle mius
twice the perimeter of hexagon must be greater than or equal -18 .
( sum of perimeters of square and triangle)-
(twice)( perimeter of hexagon ) >= -18
3x + 4x - 2( 6x ) >= -18
7x - 12x >= -18
-5x >= -18
divide each side by -5 which will change the direction of the inequality
x <= 18/5
I suppose this means that the minimum side is > 0 and < 18/5
while the maximum side length is 18/5

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