The triangles QUR and VUR are congruent, by ASA.
RU is a common side,
∠QRU =∠VRU
∠Q=∠V=90⁰, so ∠QUR =∠VUR.
The triangles are congruent, so their corresponding sides are congruent also.
QU =VU
5x+9 = 7x+1
2x = 8
x=4,
so
|UV| =7x+1=7*4+1=29
|UV| =29
