document.write( "Question 1146195: The lengths of the sides of a right angles triangle form the terms of an
\n" ); document.write( "arithmetic sequence. If the hypotenuse is 15cm in length, what is the length of
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Algebra.Com's Answer #767483 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
The sides can be represented by a-d, a, a+d where a+d = the hypotenuse = 15 cm\r\n" );
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document.write( "So the first equation comes from that:\r\n" );
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document.write( "a+d = 15\r\n" );
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document.write( "The second equation comes from the Pythagorean theorem:\r\n" );
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document.write( "(a-d)² + a² = (a+d)²\r\n" );
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document.write( "         a² = (a+d)² - (a-d)²\r\n" );
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document.write( "         a² = [(a+d)-(a-d)][(a+d)+(a-d)]\r\n" );
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document.write( "         a² = [a+d-a+d][a+d+a-d]\r\n" );
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document.write( "         a² = [2d][2a]\r\n" );
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document.write( "         a² = 4ad\r\n" );
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document.write( "   a² - 4ad = 0\r\n" );
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document.write( "  a(a - 4d) = 0\r\n" );
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document.write( "a = 0;  a - 4d = 0\r\n" );
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document.write( "             a = 4d \r\n" );
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document.write( "For a = 0,               \r\n" );
document.write( "not possible because\r\n" );
document.write( "sides of a triangle are\r\n" );
document.write( "positive numbers.        For a = 4d\r\n" );
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document.write( "                           a+d = 15\r\n" );
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document.write( "                          4d+d = 15 \r\n" );
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document.write( "                            5d = 15\r\n" );
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document.write( "                             d = 3\r\n" );
document.write( "                           \r\n" );
document.write( "                             a = 4(3)\r\n" );
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document.write( "                             a = 12\r\n" );
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document.write( "The sides are \r\n" );
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document.write( "a-d = 12-3 = 9\r\n" );
document.write( "  a = 12\r\n" );
document.write( "a+d = 12+3 = 15 (given)    9, 12, 15\r\n" );
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document.write( "Edwin
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