Answer: √3.
Explanation:
In a 45-45-90 triangle, the two legs are congruent, which means that both x and x are equal in length. The hypotenuse is √2 times the length of one of the legs.
One side is √6, so you can set up an equation like this:
x = √6 / √2
To simplify this expression, you can rationalize the denominator by multiplying both the numerator and denominator by √2:
x = (√6 / √2) * (√2 / √2)
x = (√12 / 2)
Now, simplify the square root:
x = (√(4 * 3) / 2)
x = (√4) * (√3) / 2
x = (2√3) / 2
Finally, simplify further:
x = √3
So, the measure of x is √3.