document.write( "Question 1014153: The diagonals of a rhombus are in the ratio 1:3. If each side of the rhombus is 10 cm long, find the length of the longer diagonal. \n" ); document.write( "

Algebra.Com's Answer #630519 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "The diagonals of a rhombus are in the ratio 1:3. If each side of the rhombus is 10 cm long, find the length of the longer diagonal.
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document.write( "Let x be the shorter diagonal measure, in centimeters. \r\n" );
document.write( "Then the longer diagonal is 3x long, according to the condition.\r\n" );
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document.write( "Diagonals of a rhombus bisect each other at the intersection point (it is true for any parallelogram).\r\n" );
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document.write( "Besides of it, diagonals of a rhombus are perpendicular.\r\n" );
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document.write( "So, they divide the rhombus in four congruent right-angled triangles.\r\n" );
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document.write( "Let us consider one of these four triangles.\r\n" );
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document.write( "It has the legs of  and  cm.\r\n" );
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document.write( "It has the hypotenuse of 10 units long (it is the side of the rhombus).\r\n" );
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document.write( "Thus you can write the Pythagorean Theorem in this form:\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = ,   or\r\n" );
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document.write( " = .\r\n" );
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document.write( "Hence,  =  = 40,  and  x =  = .\r\n" );
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document.write( "It is the length of the shorter diagonal.\r\n" );
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document.write( "The length of the longer diagonal is in 3 times more, or  cm.\r\n" );
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document.write( "Answer. The length of the longer diagonal is   cm.\r\n" );
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