Answer:
w = 28
x = 18
Step-by-step explanation:
To make the triangles congruent, the hypotenuse and leg need to be the same length.
5w +x -59 = -w +2x +91
4w+4x -92 = 2x +2w
These two equations can be written in general form by subtracting the right-side expression from both sides.
6w -x -150 = 0
2w +2x -92 = 0
The second of these equations can be divided by 2 to give ...
w +x -46 = 0
When that is added to the first equation, we have ...
7w -196 = 0
w -28 = 0
w = 28
Using this in our simplified second equation, we have ...
x = 46 -w = 46 -28
x = 18
_____
Additional comment
These values of w and x make the side lengths ...
UV = 2x -w +91 = 2(18) -28 +91 = 8 +91 = 99
UT = 2x +2w = 92 . . . . from 2nd equation
Using the Pythagorean theorem, this makes ...
TV = √(99^2 -92^2) = √1337 ≈ 36.57
