document.write( "Question 311575: The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18cm and a second side that is 3cm less than twice the third side, what are the possible lengths for the second and third sides? \n" ); document.write( "

Algebra.Com's Answer #222856 by Edwin McCravy(20055) $\"\"$ $\"About$

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The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 18cm and a second side that is 3cm less than twice the third side, what are the possible lengths for the second and third sides?
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document.write( "The three sides are:  \r\n" );
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document.write( "First side   = 18\r\n" );
document.write( "Third side   = x\r\n" );
document.write( "Second side  = 2x - 3\r\n" );
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document.write( "First side  + Second side > Third Side,   therefore   18 + (2x - 3) > x     \r\n" );
document.write( "First side  + Third side  > Second Side,  therefore          18 + x > 2x - 3\r\n" );
document.write( "Second side + Third side  > Second Side,  therefore    (2x - 3) + x > 18 \r\n" );
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document.write( "So we have:\r\n" );
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document.write( "Simplifying:\r\n" );
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document.write( "Simplifying further:\r\n" );
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document.write( "Simplifying further:\r\n" );
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document.write( "Simplifying further:\r\n" );
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document.write( "We can eliminate the first inequality, since the third one guarantees it\r\n" );
document.write( "because if x is greater than 7 it is CERTAILY greater than =15.\r\n" );
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document.write( "Those two inequalities can be combined as\r\n" );
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document.write( "or if we prefer:\r\n" );
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document.write( ", which is the same thing.\r\n" );
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document.write( "So the third side, x, is greater than 7 but less than 21.\r\n" );
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document.write( "Since the Second side is 2x - 3, we must build 2x - 3\r\n" );
document.write( "from the x which is in the middle of .\r\n" );
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document.write( "To make the x into a 2x, we multiply all three sides of\r\n" );
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document.write( " by 2, getting\r\n" );
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document.write( "To make the 2x into a 2x - 3, we subtract 3 from all three sides of the above:\r\n" );
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document.write( "Simplifying\r\n" );
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document.write( "So   \r\n" );
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document.write( "So the Second side, 2x - 3, is greater than 11 but less than 39.\r\n" );
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document.write( "Edwin

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