This right triangle can only be an isosceles right triangle, because if it is not an isosceles right triangle, then the lengths of the three sides are not equal and are three different numbers. Three different numbers must satisfy this quadratic equation, that is, this quadratic equation must have three different solutions, which is impossible.

Solution:

Let the right-angle side length be a and the hypotenuse length be √2a.

Then one of the two solutions of the equation is a and the other is √2a.

According to the relation theorem between roots and coefficients,

a*√2a=2√2

a=√2

√2

So the area is 1/2*√2*√2= 1.

③ First floor = (a+b) 2-(a+b) m+2 √ 2 = 0.

This step is wrong, it should be 3 = (a+b) 2-cm+2 √ 2 = 0.

So this is wrong.