Question 1019752
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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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In a parallelogram, the intersection point of diagonals bisects each diagonal.

It is very well known property of any parallelogram.
(See the lesson <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/Properties-of-diagonals-of-parallelograms.lesson>Properties of diagonals of parallelograms</A> in this site).

In particular, the point A bisects the diagonal XZ of the parallelogram WXYZ.

Therefore, |XA| = |ZA|. (The dimensions of these segments are equal each other).

It gives you an equation

3m = 5m - 4.

It implies 

4 = 5m - 3m = 2m.

Hence, m = {{{4/2}}} = 2.

Thus you just found m.

Notice that the info YW = 10m from the condition is not necessary to find m.
In opposite, you can use this info to determine the length of the diagonal YW.
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