SOLUTION: Triangle ABC is an equilateral triangle of dimension (3x-2y),(x+6y) and2(2x-3y).find the perimeter of the triangle

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Question 1164096: Triangle ABC is an equilateral triangle of dimension (3x-2y),(x+6y) and2(2x-3y).find the perimeter of the triangle
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
 
(3x-2y) = (x+6y) = 2(2x-3y)

          (3x-2y) = (x+6y) = 2(2x-3y)     

Set the first and second sides equal

3x-2y = x+6y
   2x = 8y
    x = 4y 

Set the first and third side equal

3x - 2y = 2(2x-3y)
3x - 2y = 4x - 6y
4y - x = 0
    4y = x

that the same thing

Set the second and third sides equal

x+6y = 2(2x-3y)
x+6y = 4x - 6y
12y - 3x = 0
Divide through by 3
  4y - x = 0
      4y = x

So there is not enough information given to determine
x or y, so there are infinitely many solutions. 

Edwin

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


There is no numerical value given anywhere, so we can't find the perimeter as a number. The best we can do is find the perimeter in terms of either x or y.

Use the first two expressions to get an expression for one variable in terms of the other:

3x-2y+=+x%2B6y
2x+=+8y
x+=+4y

Note that using any pair of the given expressions will lead to the same result.

So the perimeter is

3x-2y+=+3%284y%29-2y+=+12y-2y+=+10y

Of course you could also express the perimeter in terms of x only.