we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem we have that
triangle UVW and triangle UST are similar
that means
UV/US=VW/ST=UW/UT
so
UV/US=VW/ST
substitute the given values
(5x+11)/18=88/24
solve for x
24(5x+11)=18*88
120x+264=1,584
120x=1,584-264
120x=1,320
x=11