document.write( "Question 889992: if the perimeter of a rhombus is 260 c.ms and one of its diagonals is 66 c.ms , then find the other diagonal \n" ); document.write( "

Algebra.Com's Answer #538619 by Edwin McCravy(20060) $\"\"$ $\"About$

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document.write( "All four sides of a rhombus have equal measures, so each side is \r\n" );
document.write( "of the perimeter or  = 65. So we label the upper left side 65.\r\n" );
document.write( "We are given that one of the diagonals is 66. Let that be the red diagonal\r\n" );
document.write( "below. Since the diagonals bisect each other the top half of the red \r\n" );
document.write( "diagonal is  of 66 or 33.  So we label the top half of the red\r\n" );
document.write( "diagonal 33.  We want to know the length of the green diagonal.  So\r\n" );
document.write( "we label the left half of the green diagonal x.\r\n" );
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document.write( "Since the diagonals of a rhombus are perpendicular, the triangle with\r\n" );
document.write( "the sides x,33, and 65 is a right triangle, so we can use the Pythagorean\r\n" );
document.write( "theorem to find x:\r\n" );
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document.write( " x² + 33² = 65²\r\n" );
document.write( "x² + 1089 = 4225\r\n" );
document.write( "       x² = 3136\r\n" );
document.write( "        x = √3136\r\n" );
document.write( "        x = 56\r\n" );
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document.write( "So half the green diagonal is 56 cm.\r\n" );
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document.write( "Therefore, the whole green diagonal is 2×56 = 112 cm.\r\n" );
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document.write( "Edwin

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