document.write( "Question 120044: 20 triangles measuring 3 x 6 assemble into a square \n" ); document.write( "
Algebra.Com's Answer #87991 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
Solution by Edwin:
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\n" ); document.write( "20 triangles measuring 3 x 6 assemble into a square
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document.write( "20 RIGHT triangles with legs measuring 3 and 6 can be \r\n" );
document.write( "assembled into a square this way.\r\n" );
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document.write( "Let's calculate the length of the hypotenuse of each\r\n" );
document.write( "of those right triangles using the Pythagorean theorem.\r\n" );
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document.write( "c² = a² + b²\r\n" );
document.write( "c² = 3² + 6²\r\n" );
document.write( "c² = 9 + 36\r\n" );
document.write( "c² = 45\r\n" );
document.write( "c = \"sqrt%2845%29\"\r\n" );
document.write( "c = \"sqrt%289%2A5%29\"\r\n" );
document.write( "c = \"3sqrt%285%29\"\r\n" );
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document.write( "Each of the 20 right triangle has an area calculated by\r\n" );
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document.write( "A = \"1%2F2\"bh = \"1%2F2\"(3)(6) = 9 square units\r\n" );
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document.write( "The area of the square must be 20 times as much as\r\n" );
document.write( "the area of one triangle, or 9x20 or 180 square units.\r\n" );
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document.write( "We can now calculate the side of the square by using the\r\n" );
document.write( "formula for the area of a square,\r\n" );
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document.write( "A = \"s%5E2\" \r\n" );
document.write( "180 = \"s%5E2\"\r\n" );
document.write( "Taking square roots of both sides,\r\n" );
document.write( "\"sqrt%28180%29\" = \"sqrt%28s%5E2%29\"\r\n" );
document.write( "\"sqrt%2836%2A5%29\" = \"s\"\r\n" );
document.write( "\"6sqrt%285%29\" = \"s\"\r\n" );
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document.write( "Therefore each side of the square, being\r\n" );
document.write( "\"6sqrt%285%29\", is twice the hypotenuse of\r\n" );
document.write( "each triangle, which is \"3sqrt%285%29\".\r\n" );
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document.write( "Let's draw that square:\r\n" );
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document.write( "So we place two triangles on each side, 8\r\n" );
document.write( "triangles in all, with their hypotenuses \r\n" );
document.write( "along the side of a square like this:  \r\n" );
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document.write( "Then draw 4 more line segments, making a smaller square\r\n" );
document.write( "in the middle of the big square, and 4 rectangles\r\n" );
document.write( "around it like this:\r\n" );
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document.write( "Notice that the square in the middle is a 6x6\r\n" );
document.write( "square and the 4 rectangles around it are 3x6\r\n" );
document.write( "rectangles.\r\n" );
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document.write( "Now we can split the 6x6 square into 2 3x6 rectangles,\r\n" );
document.write( "like this:\r\n" );
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document.write( "Now we have 6 3x6 rectangles each of which can be split \r\n" );
document.write( "into 2 right triangles with legs 3 and 6, by drawing in a \r\n" );
document.write( "diagonal of each, like this:\r\n" );
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document.write( "That's it!  Count the rectangles.  They're 20 of them.\r\n" );
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document.write( "Edwin
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