document.write( "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?
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Algebra.Com's Answer #834981 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "The side lengths of triangle ABC are 22, 2x, and 55.
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\n" ); document.write( "If so, find the value of $x$ that makes the triangles similar. If not, leave this part blank.
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document.write( "(1)  From triangle inequalities, applied to triangle ABC, we have this inequality\r\n" );
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document.write( "         2x > 55 - 22  (any side of a triangle is longer than the difference of the two other sides).\r\n" );
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document.write( "     It implies  2x > 33,  or  x >  = 16.5.\r\n" );
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document.write( "(2)  From triangle inequalities, applied to triangle DEF, we have this inequality\r\n" );
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document.write( "         5.5x < 11 + 5  (any side of a triangle is shorter than the sum of the two other sides).\r\n" );
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document.write( "    It implies  5.5x < 16,  or  x <  = 2.909090909...\r\n" );
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document.write( "It is not possible that these two inequalities be held together simultaneously \r\n" );
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document.write( "(this system has no solutions), so the triangles are NOT similar.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with complete explanations.\r
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\n" ); document.write( "\n" ); document.write( "As I notice from your post, you systematically use all punctuation signs (dots and commas) INCORRECTLY.\r
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\n" ); document.write( "\n" ); document.write( "Neither dots nor commas require using blank space before them. It only makes reading more complicated.\r
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