Is the answer only 1?

Yes...

The Jock wrote:In the figure below, segments RS and TU represent two
positions of the same support beam leaning against the
side SV of a structure. The length TV is how much greater
than the length RV ?
(1) The length of SU is 2underroot2 - 4 meters.
(2) The ratio of the length of V R to V T is underroot6 : 2.




I know that the given triangles are 45:45:90 and 30:60:90 triangles. But I need some more explanation...

Okay the lengths SR=UT and suppose they are equal to 2x.squareroot6. (for easier calculations)
So 45-45-90 triangle gives us; UV=VT=2x.squareroot3
30-60-90 triangle gives us; VR=x.sqaureroot6 and SV=3x.squareroot2.

So all we need to know is x. Then we can find the length of any line in this image. Using Option (1), we can find X because we know SV and UV,but option (2) does not give us anything we dont know. Because we already know the ratio of VR to VT.

The Jock wrote:In the figure below, segments RS and TU represent two
positions of the same support beam leaning against the
side SV of a structure. The length TV is how much greater
than the length RV ?
(1) The length of SU is 2underroot2 - 4 meters.
(2) The ratio of the length of V R to V T is underroot6 : 2.




I know that the given triangles are 45:45:90 and 30:60:90 triangles. But I need some more explanation...

@Nathan and Jock

The logic used by Nathan looks spot on. I have one issue though, 2sqrt2 - 4 per stmt 1 is a negative number hence the numbers need to be relooked at.......