.
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document.write( "Let x be the common length of the square and the rhombus.\r\n" );
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document.write( "Use the formula for the rhombus area \r\n" );
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document.write( " Rhombus area = 
= 
,\r\n" );
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document.write( "where 
is the angle between (any) two adjacent sides of the rhombus.\r\n" );
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document.write( "Comparing with the formula for the square area, you can conclude that 
= 
;\r\n" );
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document.write( "hence, the angle is either 30° or 150°, which geometrically represent the same rhombus.\r\n" );
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document.write( "Then the longer diagonal of the rhombus is ( the law of cosine with cos(150°) = 
)\r\n" );
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document.write( " 
= 
= 
= 
.\r\n" );
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document.write( "The shorter diagonal is ( the law of cosine with cos(30°) = 
)\r\n" );
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document.write( " 
= 
= 
= 
.\r\n" );
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document.write( "Thus the ratio of the longer diagonal length to the shorter diagonal length is 
.\r\n" );
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document.write( "You can rationalize this fraction further\r\n" );
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document.write( " = .
= 
= 
= 
= 3.732 (approximately).\r\n" );
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document.write( "Solved.\r
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document.write( "Nice solution to a nice problem.\r
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document.write( "![\"\"](\"/images/stars/stars-13.gif\")
