The value of r is 12.
This is because the line segment DM is made up of two segments, DG and GM.
We are given that the length of DM is 25, and the lengths of DG and GM are r+2 and 2r-13, respectively.
Therefore, we can set up the following equation:
r+2 + 2r-13 = 25
Combining like terms, we get:
3r - 11 = 25
Adding 11 to both sides, we get:
3r = 36
Dividing both sides by 3, we get:
r = 12
Therefore, the value of r is 12.
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