Note that we have similar triangles, such that :
BDA ≈ BAC ....so....
BA/DA = BC/AC
And BC = sqrt(10^2 + 20^2) = sqrt(500) = 10sqrt(5) .......so....
10/DA = 10sqrt(5) /20
10/DA = sqrt(5) / 2 cross-multiply
20 = sqrt(5) * DA
DA = 20/sqrt(5) = 20sqrt(5) / 5 = 4sqrt(5) → (C)