Answer: Choice D
[tex]\frac{9\sqrt{2}}{2}[/tex]
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Explanation:
We have a 45-45-90 triangle. If x is the leg length, then y = x*sqrt(2) is the hypotenuse.
Solving for y gets us [tex]x= \frac{y}{\sqrt{2}} = \frac{y\sqrt{2}}{2}[/tex]
In this case, y = 9 is the hypotenuse which then leads to choice D.
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Another way to find the answer is to use the pythagorean theorem
a = x and b = x are the two congruent legs
c = 9 is the hypotenuse
Solving a^2+b^2 = c^2, aka x^2+x^2 = 9^2, will lead to [tex]x = \frac{9\sqrt{2}}{2}[/tex]
