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
Answer by ikleyn(52781)   (Show Source):
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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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Since the diagonals of a parallelogram bisect each other at the intersection point, we have an equation
|PM| = |PK| (these segments are halves of the diagonal KM).
It gives
3x - 2 = x + 3 ---> 2x = 5, x = 2.5 units of length.
Due to the same reason,
|PL| = |PJ| (these segments are halves of the diagonal LJ).
Hence, |PL| = |PJ| = 4x - 3 = 4*2.5 - 3 = 10 - 3 = 7.
Answer. The length of PL is 7 units.
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