Find x.
geometry math question

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