Triangle XYZ is an isosceles right triangle.
Let's sketch an isosceles right triangle:


Side XY is longer than side YZ
Since the hypotenuse is the longest side of a right triangle, side XY must be the hypotenuse. Add this to our diagram:


This also means the last remaining vertex must be Z:


The area of the triangle is 16. What is the measure of side XY?
Let j = the length of side ZY,
Since ZY = ZX, we can see that side ZX must also halve length j


Area of triangle = (base)(height)/2
So, we can write: 16 = (j)(j)/2
Simplify: 16 = j²/2
Multiply both sides by 2 to get: 32 = j²
Solve: j = √32

What is the measure of side XY?
Our diagram now looks like this.


Applying the Pythagorean Theorem, we can write: (√32)² + (√32)² = c²
Simplify: 32 + 32 = c²
Simplify: 64 = c²
Solve: c = 8

Answer: C

Cheers,
Brent

Let's break down the given information:
1) The triangle is an isosceles triangle, which means 2 sides have equal length.
2) Side XY is greater than YZ -> this means that the side XY is the hypotenuse because in a right-angled triangle, the hypotenuse is always the biggest side and it also is an isosceles triangle. Hence, XY is the hypotenuse.
3) The area of the triangle is 16
X
|\
| \
|__\
Z ....Y

Area of triangle = base*height/2
16=ZY*XZ/2
as XZ=ZY we can write
16=XZ*XZ/2
16*2=XZ^2
XZ^2=32
XZ=root(32)
XZ=4root(2)

As it is a 45-45-90 triangle that means the sides are in ratio 1:1:root2

So 4root2 * root2 = 8

Answer is C