document.write( "Question 1045328: 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 17 cm and a second side that is 4 cm less than twice the third side, what are the possible lengths for the second and third sides? \n" ); document.write( "

Algebra.Com's Answer #660736 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "The sum of the lengths of any two sides of a triangle must be greater than the third side.
\n" ); document.write( "If a triangle has one side that is 17 cm and a second side that is 4 cm less than twice the third side,
\n" ); document.write( "what are the possible lengths for the second and third sides?
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document.write( "Let x be the length o the third side.\r\n" );
document.write( "Then the length of the second side is (2x-4).\r\n" );
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document.write( "According to the \"triangle inequalities\", these three inequalities should be in the place\r\n" );
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document.write( "17 + (2x-4) > x,    (1)\r\n" );
document.write( "(2x-4) + x > 17,    (2)\r\n" );
document.write( "17 + x    > 2x-4.   (3)\r\n" );
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document.write( "Inequality (1) is always valid and does not bring any restrictions.\r\n" );
document.write( "Inequality (2) is x >  = 7.\r\n" );
document.write( "Inequality (3) is x < 21.\r\n" );
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document.write( "Answer. The third side length must be between 7 and 21 (excluding the ends). \r\n" );
document.write( "        The second side must be longer than 7. In addition, the second side must be \"4 cm less than twice the third side\". \r\n" );
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