document.write( "Question 1014154: The diagonals of a parallelogram JKLM intersect at P. If PM=3x-2, PK=x+3, and PJ=4x-3, find the length of PL \n" ); document.write( "

Algebra.Com's Answer #630517 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The diagonals of a parallelogram JKLM intersect at P. If PM=3x-2, PK=x+3, and PJ=4x-3, find the length of PL
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document.write( "Since the diagonals of a parallelogram bisect each other at the intersection point, we have an equation\r\n" );
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document.write( "|PM| = |PK|  (these segments are halves of the diagonal KM).\r\n" );
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document.write( "It gives\r\n" );
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document.write( "3x - 2 = x + 3  --->  2x = 5, x = 2.5 units of length.\r\n" );
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document.write( "Due to the same reason, \r\n" );
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document.write( "|PL| = |PJ|   (these segments are halves of the diagonal LJ).\r\n" );
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document.write( "Hence, |PL| = |PJ| = 4x - 3 = 4*2.5 - 3 = 10 - 3 = 7.\r\n" );
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document.write( "Answer. The length of PL is 7 units.\r\n" );
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