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For starters you know two sides are equal since a right isoceles triangle has two equal sides. The perimeter formula for a triangle is A + B + C = P or for this problem: 16 + 16√2 = P Also, you know the sides are in the ratio 1:1:√2. So there are two possible answers:
1. The two short sides of the triangle add up to 16. Thus the hypotenuse is 16√2. We can check by using the pythagorean theorem.
8^2 + 8^2 = (16√2)^2
64 + 64 = (256 * 2), obviously this does not add up
2. The second option is that 16 is the hypotenuse and (16√2) is the length of each short side. Therefore each side would be 8√2.