AMC 10B 2025 (Problem 6)

The line

y=\frac{1}{3}x+1

divides the square region defined by

0\le x\le2

and

0\le y\le2

into an upper and lower region. The line

x=a

divides the lower region into two regions of equal area. Then

a

can be written as

\sqrt{s}-t

, where

s

and

t

are positive integers. What is

s+t

\text{(A)}\;18

\text{(B)}\;19

\text{(C)}\;20

\text{(D)}\;21

\text{(E)}\;22