document.write( "Question 705170: A triangle has a perimeter of 102 in. The shortest side measures 6 inches less than the middle side. The longest side is 4 less than twice the middle side. Find the lengths of all three sides. \n" ); document.write( "
Algebra.Com's Answer #434433 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there--\r\n" );
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document.write( "PROBLEM:\r\n" );
document.write( "A triangle has a perimeter of 102 in. The shortest side measures 6 inches less than the \r\n" );
document.write( "middle side. The longest side is 4 less than twice the middle side. Find the lengths of all \r\n" );
document.write( "three sides. \r\n" );
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document.write( "SOLUTION:\r\n" );
document.write( "Let x be the length of the middle side.\r\n" );
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document.write( "The shortest side is 6 inches less than the middle side, or x-6.\r\n" );
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document.write( "The longest side is 4 less than twice the middle side, or 2x-4.\r\n" );
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document.write( "The perimeter (the sum of the side lengths) is 102, so\r\n" );
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document.write( "x + (x-6) + (2x-4) = 102\r\n" );
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document.write( "Solve for x to find the length of the middle side. Combine like terms: x+x+2x is 4x, and\r\n" );
document.write( "-6 + -4 is -10.\r\n" );
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document.write( "4x - 10 = 102\r\n" );
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document.write( "Add 10 to both sides.\r\n" );
document.write( "4x = 112.\r\n" );
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document.write( "Divide both sides by 4.\r\n" );
document.write( "x = 28\r\n" );
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document.write( "The middle side is 28 inches.\r\n" );
document.write( "The shortest side is 6 inches less, or 22 inches,\r\n" );
document.write( "The longest side is 4 less than twice 28, or 52 inches.\r\n" );
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document.write( "Check that the sum of these side lengths is 102 inches.\r\n" );
document.write( "28 + 22 + 52 = 102. Check!\r\n" );
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document.write( "That's it,\r\n" );
document.write( "Ms. Figgy\r\n" );
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