Verified answer

An isosceles right triangle MUST be a 90-45-45 triangle. These always have sides in the ratio

√2: 1: 1 where the √2 side is the hypotenuse.

In order for these sides to be in the required ration, given the hypotenuse is 3√2, the other two sides must be 3 millimetres each.

Now, the perimeter of a triangle is the sum of the three side lengths,

3 mm + 3 mm + 3√2 mm

= 6 + 3√2 mm which cannot be simplified further.