document.write( "Question 205479: Suppose you need to construct a right triangle in which the shortest side is eight feet less than the largest side and the third side is seven feet more than the shortest side. \n" ); document.write( "
Algebra.Com's Answer #155093 by Edwin McCravy(20055)\"\" \"About 
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Suppose you need to construct a right triangle in which the shortest side is eight feet less than the largest side and the third side is seven feet more than the shortest side.
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document.write( "\"Smallest+=+Longest+-+8\"\r\n" );
document.write( "\"Middle+=+Smallest+%2B+7\"\r\n" );
document.write( "\"Smallest%5E2+%2B+Middle%5E2+=+Longest%5E2\"\r\n" );
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document.write( "\"system%28S=L-8%2CM=S%2B7%2CS%5E2%2BM%5E2=L%5E2%29\"\r\n" );
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document.write( "Substitute \"L-8\" for \"S\" in \"M=S%2B7\"\r\n" );
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document.write( "\"M=S%2B7\"\r\n" );
document.write( "\"M=%28L-8%29%2B7\"\r\n" );
document.write( "\"M=L-8%2B7\"\r\n" );
document.write( "\"M=L-1\"\r\n" );
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document.write( "Substitute \"L-8\" for \"S\" and \"L-1\" for M in \"S%5E2%2BM%5E2=L%5E2\"\r\n" );
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document.write( "\"S%5E2%2BM%5E2=L%5E2\"\r\n" );
document.write( "\"%28L-8%29%5E2%2B%28L-1%29%5E2=L%5E2\"\r\n" );
document.write( "\"%28L-8%29%28L-8%29%2B%28L-1%29%28L-1%29=L%5E2\"\r\n" );
document.write( "\"%28L%5E2-8L-8L%2B64%29%2B%28L%5E2-L-L%2B1%29=L%5E2\"\r\n" );
document.write( "\"%28L%5E2-16L%2B64%29%2B%28L%5E2-2L%2B1%29=L%5E2\"\r\n" );
document.write( "\"L%5E2-16L%2B64%2BL%5E2-2L%2B1=L%5E2\"\r\n" );
document.write( "\"2L%5E2-18L%2B65=L%5E2\"\r\n" );
document.write( "\"L%5E2-18L%2B65=0\"\r\n" );
document.write( "\"%28L-13%29%28L-5%29=0\"\r\n" );
document.write( "\"L-13=0\"   \"L-5=0\"\r\n" );
document.write( "   \"L=13\"    \"L=5\"\r\n" );
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document.write( "So the longest side is 13 ft or 5 ft\r\n" );
document.write( "But we must check:\r\n" );
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document.write( "Substituting \"L=13\"   \r\n" );
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document.write( "\"Smallest+=+Longest+-+8+=+13-8=5\"\r\n" );
document.write( "\"Middle+=+Smallest+%2B+7=5%2B7=12\"\r\n" );
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document.write( "That's one solution. Longest = 13 ft, Middle = 12 ft, Longest = 13 ft.\r\n" );
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document.write( "Substituting \"L=5\"   \r\n" );
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document.write( "\"Smallest+=+Longest+-+8+=+5-8=-3\"\r\n" );
document.write( "\"Middle+=+Smallest+%2B+7=-3%2B7=4\"\r\n" );
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document.write( "That would require a triangle to have a negative side,\r\n" );
document.write( "so we discard that as a solution.\r\n" );
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document.write( "Edwin
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