document.write( "Question 182836: A rhombus has one diagonal equal to the sides. The other diagonal has length 60. How long are the sides? \n" ); document.write( "

Algebra.Com's Answer #137283 by Edwin McCravy(20081) $\"\"$ $\"About$

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A rhombus has one diagonal equal to the sides.
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document.write( "Here is the rhombus ABCD, with diagonal AC equal to the sides,\r\n" );
document.write( "we let each side and the diagonal have length s: \r\n" );
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document.write( "The rhombus therefore consiste of two equilateral\r\n" );
document.write( "triangles with a common side AC. \r\n" );
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\n" ); document.write( "The other diagonal has length 60.
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document.write( "So we draw the other diagonal DB, intersecting\r\n" );
document.write( "the first diagonal at point E. Since the\r\n" );
document.write( "diagonals of any parallogram bisect each other,\r\n" );
document.write( "and since a rhombus is a parallelogram, the top\r\n" );
document.write( "and bottom halves of diagonal DB are half of 60,\r\n" );
document.write( "So DE = EB = 30.  Also AE = EC = : \r\n" );
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document.write( "Since the diagonals of a rhombus are also perpendicular,\r\n" );
document.write( "triangle AED is a right triangle, so we can use the\r\n" );
document.write( "Pythagorean theorem.  (We could use any one of the\r\n" );
document.write( "four right triangles since all four are congruent.)\r\n" );
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document.write( "or each side s is about 34.64101615.\r\n" );
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document.write( "Edwin

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