Answer:
12 - 2√11 = BS or 5.367..... ≅ BS
Explanation:
Find ST using Pythagorean theorem
a^2 + b^2 = c^2
(6+18)^2 + 12^2 = c^2
576 + 144 = c^2
√720 = c
similar triangle by a factor of three so BC = √720/3 or √80
Find BU using Pythagorean theorem (BU = a in this case)
a^2 + b^2 = c^2
(√80)^2 - 6^2 = a^2
a = √44
12 - √44 = BS
12 - 2√11 = BS or 5.367..... ≅ BS