document.write( "Question 1019752: WXYZ is a parallelogram with diagonals XZ and YW that intersect at point A. If XA = 3m and ZA = 5m-4, and YW = 10m, find 'm'. \n" ); document.write( "

Algebra.Com's Answer #635716 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "WXYZ is a parallelogram with diagonals XZ and YW that intersect at point A. If XA = 3m and ZA = 5m-4, and YW = 10m, find 'm'.
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document.write( "In a parallelogram, the intersection point of diagonals bisects each diagonal.\r\n" );
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document.write( "It is very well known property of any parallelogram.\r\n" );
document.write( "(See the lesson Properties of diagonals of parallelograms in this site).\r\n" );
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document.write( "In particular, the point A bisects the diagonal XZ of the parallelogram WXYZ.\r\n" );
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document.write( "Therefore, |XA| = |ZA|. (The dimensions of these segments are equal each other).\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( "3m = 5m - 4.\r\n" );
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document.write( "It implies \r\n" );
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document.write( "4 = 5m - 3m = 2m.\r\n" );
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document.write( "Hence, m =  = 2.\r\n" );
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document.write( "Thus you just found m.\r\n" );
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document.write( "Notice that the info YW = 10m from the condition is not necessary to find m.\r\n" );
document.write( "In opposite, you can use this info to determine the length of the diagonal YW.\r\n" );
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