Triangle on the right is 30 60 90 triangle
The ratio of short leg : long leg : hypotenuse = a : a√3 : 2a
Given long leg = 8√2
so short leg = 8√2 / √3 = 8√2 *√3 / √3 *√3 = 8√6/ 3
Hypo = 2 (8√6/ 3) = 16√6/ 3
The triangle on the left is 45 45 90 triangle
Ratio of leg : hypotenuse = a : a√2
The hypotenuse of triangle on the right is the leg of triangle on the left
so a = 16√6/ 3
Hypotenuse, x = (16√6/ 3) √2 = 16√12 / 3 = 32√3 / 3
Answer is B.
32√3 / 3
