SOLUTION: In rectangle ABCD, a point M is selected inside the rectangle. If AM=4, BM=5, and CM=6, find the length of DM.

Question 911998: In rectangle ABCD, a point M is selected inside the rectangle. If AM=4, BM=5, and CM=6, find the length of DM.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Let the coordinates of A be (0,0).
Then B would be (0,xb), C would be (xc,yc), and D would be (xd,0).
Calculate the distance from each vertex to M.
AM:

1.
BM:
2.
CM:
3.
DM:
4. where is the unknown distance.
First we can simplify since,
and
So then, for CM,
3.
and for DM,
4.
Substituting from 3 into 4.

Then substituting from 2,

Finally, substituting from 1,

.
.
.

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