SOLUTION: The side lengths of triangle ABC are 22 , 2x , and 55 . The side lengths of triangle DEF are 11 ,5 , and 5.5x . Is it possible that the triangles are similar? If so, find the valu

Question 1200762: The side lengths of triangle ABC are 22 , 2x , and 55 . The side lengths of triangle DEF are 11 ,5 , and 5.5x . Is it possible that the triangles are similar?
If so, find the value of $x$ that makes the triangles similar. If not, leave this part blank.

Answer by ikleyn(52780) (Show Source): You can put this solution on YOUR website!
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The side lengths of triangle ABC are 22, 2x, and 55.
The side lengths of triangle DEF are 11, 5, and 5.5x.
Is it possible that the triangles are similar?
If so, find the value of $x$ that makes the triangles similar. If not, leave this part blank.
~~~~~~~~~~~~~~~~~

(1)  From triangle inequalities, applied to triangle ABC, we have this inequality

         2x > 55 - 22  (any side of a triangle is longer than the difference of the two other sides).


     It implies  2x > 33,  or  x >  = 16.5.




(2)  From triangle inequalities, applied to triangle DEF, we have this inequality

         5.5x < 11 + 5  (any side of a triangle is shorter than the sum of the two other sides).


    It implies  5.5x < 16,  or  x <  = 2.909090909...



It is not possible that these two inequalities be held together simultaneously 

(this system has no solutions), so the triangles are NOT similar.

Solved, with complete explanations.

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As I notice from your post, you systematically use all punctuation signs (dots and commas) INCORRECTLY.

Neither dots nor commas require using blank space before them. It only makes reading more complicated.

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