I think 16 is the right answer.

Let x be the length of the hypotenuse. Then, since we are dealing with a 45-45-90 triangle, the lengths of the other 2 sides are each (x/sqrt(2)).

So, the perimeter of the triangle will be x+(2x)/sqrt(2). We are given the perimeter, so we can set this equation equal to 16+16sqrt(2) and solve for x.

x+(2x)/sqrt(2) = 16+16sqrt(2)

x(1+2/sqrt(2)) = 16(1+sqrt(2))

x(1+sqrt(2)) = 16(1+sqrt(2))

x=16

To double check, the perimeter of a 45-45-90 triangle with hypotenuse of 16 will be

16+16/sqrt(2)+16/sqrt(2) = 16+32/sqrt(2) = 16+(32sqrt(2))/2
= 16 + 16sqrt(2),

which matches the perimeter given in the question

Thanks I can see that, so simple, great expanation.