The length of side AB is (√2 / 2)√22.
In a 45-45-90 triangle ABC, the ratio of the lengths of the sides is x : x : x√2.
Since side BC is √11, we can set up the equation x√2 = √11, and solve for x.
Dividing both sides of the equation by √2, we get x = √11/√2.
Rationalizing the denominator by multiplying both the numerator and denominator by √2, we get x = (√11 x √2) / (√2 x √2)
x= √22/2
x = (√2 x √11) / 2
x = (√22 / 2)√2
x = (√2 / 2)√22.
Therefore, side AB is (√2 / 2)√22.
The probable question may be:
IN 45-45-90 triangle ABC, side AB=x, side BC=\sqrt11, Find the length of side AB