document.write( "Question 1089943: if the perimeter of a rhombus is 40 cm and one of its diagonals is 12cm, find the other diagonal \n" ); document.write( "

Algebra.Com's Answer #704331 by ikleyn(52782) $\"\"$ $\"About$

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document.write( "1.  Since the sides of each rhombus have the same measures, the side length is  of the perimeter, i.e. 10 cm.\r\n" );
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document.write( "2.  In each rhombus, diagonals divide it in four congruent right-angled triangles.\r\n" );
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document.write( "    As we just found, the hypotenuse of each such triangle is 10 cm.\r\n" );
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document.write( "    One leg of each such triangle is half of the diagonal of 12 cm long, i.e. has the length of 6 cm.\r\n" );
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document.write( "3.  Thus we have a right-angled triangle with the hypotenuse of 10 cm and one leg of 6 cm.\r\n" );
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document.write( "    Hence, the other leg is  = 8 cm long.\r\n" );
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document.write( "4.  Then the length of the other diagonal of the rhombus is twice 8 cm, i.e. 16 cm.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The other diagonal is 16 cm long.\r
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\n" ); document.write( "\n" ); document.write( "On properties of rhombis, see the lesson\r
\n" ); document.write( "\n" ); document.write( "    - Diagonals of a rhombus are perpendicular\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( "    GEOMETRY - YOUR ONLINE TEXTBOOK \r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook under the topic \"Properties of rhombis\".\r
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