document.write( "Question 253712: Find the range for the measure of the third side of a triangle given the measures of two sides.\r
\n" ); document.write( "\n" ); document.write( "1. 5 and 9\r
\n" ); document.write( "\n" ); document.write( "2. 7 and 14\r
\n" ); document.write( "\n" ); document.write( "3. 8 and 13\r
\n" ); document.write( "\n" ); document.write( "4. 10 and 12\r
\n" ); document.write( "\n" ); document.write( "5. 12 and 15\r
\n" ); document.write( "\n" ); document.write( "6. 15 and 27\r
\n" ); document.write( "\n" ); document.write( "7. 17 and 28 \r
\n" ); document.write( "\n" ); document.write( "8. 18 and 22 \n" ); document.write( "
Algebra.Com's Answer #186047 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
1. 5 and 9
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document.write( "Let side a = 5.  Let side b = 9.  Then the triangle has\r\n" );
document.write( "sides\r\n" );
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document.write( "a=5, b=9, and c=?.  Any side of a triangle must be less \r\n" );
document.write( "than the other two sides added together, so\r\n" );
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document.write( "a < b+c, b < a+c, and c < a+b\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( " 5 < 9+c, 9 < 5+c, and c < 5+9\r\n" );
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document.write( "Solving all three for c:\r\n" );
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document.write( "-4 < c, 4 < c, c < 14\r\n" );
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document.write( "The first one is of course true, so ignore it.\r\n" );
document.write( "Put the second and third together and get \r\n" );
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document.write( "4 < c < 14\r\n" );
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document.write( "That's it. c must be more than 4 and less than 14.\r\n" );
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document.write( "--------------------------------  \r\n" );
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\n" ); document.write( "2. 7 and 14
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document.write( "Let side a = 7.  Let side b = 14.  Then the triangle \r\n" );
document.write( "has sides\r\n" );
document.write( "\r\n" );
document.write( "a=7, b=14, and c=?.  Any side of a triangle must be less \r\n" );
document.write( "than the other two sides added together, so\r\n" );
document.write( "\r\n" );
document.write( "a < b+c, b < a+c, and c < a+b\r\n" );
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document.write( "Substituting:\r\n" );
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document.write( "7 < 14+c, 14 < 7+c, and c < 7+14\r\n" );
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document.write( "Solving all three for c:\r\n" );
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document.write( "-7 < c, 7 < c, c < 21\r\n" );
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document.write( "The first one is of course true, so ignore it.\r\n" );
document.write( "Put the second and third together and get \r\n" );
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document.write( "7 < c < 21\r\n" );
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document.write( "That's it. c must be more than 7 and less than 21.\r\n" );
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\n" ); document.write( "3. 8 and 13
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document.write( "Let side a = 8.  Let side b = 13.  Then the triangle \r\n" );
document.write( "has sides\r\n" );
document.write( "\r\n" );
document.write( "a=8, b=13, and c=?.  Any side of a triangle must be less \r\n" );
document.write( "than the other two sides added together, so\r\n" );
document.write( "\r\n" );
document.write( "a < b+c, b < a+c, and c < a+b\r\n" );
document.write( "\r\n" );
document.write( "Substituting:\r\n" );
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document.write( "8 < 13+c, 13 < 8+c, and c < 8+13\r\n" );
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document.write( "Solving all three for c:\r\n" );
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document.write( "-5 < c, 5 < c, c < 21\r\n" );
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document.write( "The first one is of course true, so ignore it.\r\n" );
document.write( "Put the second and third together and get \r\n" );
document.write( "\r\n" );
document.write( "5 < c < 21\r\n" );
document.write( "\r\n" );
document.write( "That's it. c must be more than 5 and less than 21.\r\n" );
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document.write( "-------------------------------------------\r\n" );
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\n" ); document.write( "4. 10 and 12
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document.write( "Let side a = 10.  Let side b = 12.  Then the triangle \r\n" );
document.write( "has sides\r\n" );
document.write( "\r\n" );
document.write( "a=10, b=12, and c=?.  Any side of a triangle must be less \r\n" );
document.write( "than the other two sides added together, so\r\n" );
document.write( "\r\n" );
document.write( "a < b+c, b < a+c, and c < a+b\r\n" );
document.write( "\r\n" );
document.write( "Substituting:\r\n" );
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document.write( "10 < 12+c, 12 < 10+c, and c < 10+12\r\n" );
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document.write( "Solving all three for c:\r\n" );
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document.write( "-2 < c, 2 < c, c < 22\r\n" );
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document.write( "The first one is of course true, so ignore it.\r\n" );
document.write( "Put the second and third together and get \r\n" );
document.write( "\r\n" );
document.write( "2 < c < 22\r\n" );
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document.write( "That's it. c must be more than 2 and less than 22.\r\n" );
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document.write( "They are all done the same way. You can do the other half\r\n" );
document.write( "by yourself.\r\n" );
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document.write( "Edwin
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