Which value of x would make SUV TUW by HL?

By HL similarity theorem, the hypothesus and one leg of both triangles are congruent.

In the given figure, it is shown that the legs UV and UW are congruent (equivalent).

The hypothenus of triangle SUV is 2x + 9 and the hypothenus of triangle TUW is 4x - 1. For both hypothenuses to be congruent, 2x + 9 = 4x - 1

4x - 2x = 9 + 1

2x = 10

x = 5.

Therefore, the value of x, for which SUV is congruent to TUW by HL is 5.