document.write( "Question 626310: Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12. \n" ); document.write( "

Algebra.Com's Answer #394099 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find the length of a diagonal of a rhombus when the area is 48 and the other diagonal is 12.
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document.write( "Let the rhombus be ABCD with diagonal AC given = 12, and we are\r\n" );
document.write( "to find the length of diagonal BD:\r\n" );
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document.write( "The diagonals of a rhombus are perpendicular bisectors of each\r\n" );
document.write( "other.  Therefore since AC is given equal to 12, AE = EC = 6.\r\n" );
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document.write( "Since triangle ABD and CBD are congruent, and the entire rhombus\r\n" );
document.write( "has area 48, each of those triangles has area 24.\r\n" );
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document.write( "Area of triangle ABD = base×height\r\n" );
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document.write( "                  24 = BD·AE\r\n" );
document.write( "                  24 = BD·6\r\n" );
document.write( "                  24 = 3·BD\r\n" );
document.write( "                   8 = BD\r\n" );
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document.write( "Edwin

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