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Since the triangle is isoceles and right, then we know that the two legs are equal in length and we also know that the ratio of the sides is 1:1:(rt2).

This means that, if we let x=the length of one of the legs, we know that:

x + x + (rt2)x = 16+16(rt2)
(2+(rt2))x = 16(1+rt2)
x = 16(1+rt2)/(2+rt2)
x = 16/(rt2)

Then just multiply by (rt2) to get the length of the hypotenuse, which is 16.

(1+rt2)/(2+rt2)
= (rt2)(1+rt2)/ (rt2)(2+rt2) - multiplying by rt2/rt2 is like multiplying by 1.
= rt2+2/2rt2+2
= 1(rt2+2)/rt2(2+rt2) - then cancel the like term (rt2+2)
=1/rt2

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