SOLUTION: 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'.

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'.
Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
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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 Properties of diagonals of parallelograms 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 =  = 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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