Answer:
x = 16 units
Explanation:
∆ABC is a 45-45-90 triangle, and ∆BCD is a 30-60-90 triangle.
If side opposite of 90° [∆] = x, side opposite of 45° [∆] = x / √2 = x √ 2 / 2.
Given side AC is opposite of 90° [∆ABC] = 32 √ 2, side opposite of 45° [∆ABC] = 32 √ 2 / √ 2 = 32 which is AB or BC.
Since side BC is part of BCD.
Side opposite of 90° [∆BCD] = BC = 32.
Since x is opposite of 30° [∆BCD].
x = Side opposite of 90° [∆BCD] / 2 = 32 / 2 = 16.