Answer: [tex]y = 6\sqrt{2}[/tex]
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Explanation:
The value of x = 6 since the two legs of a 45-45-90 triangle are always the same length. This triangle is isosceles.
The hypotenuse of any 45-45-90 triangle is exactly [tex]\sqrt{2}[/tex] times larger compared to the leg length.
This means,
[tex]y = x\sqrt{2}\\\\y = 6\sqrt{2}[/tex]
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We can use the pythagorean theorem to confirm this
[tex]a^2 + b^2 = c^2\\\\6^2 + x^2 = y^2\\\\6^2 + 6^2 = y^2\\\\72 = y^2\\\\y^2 = 72\\\\y = \sqrt{72}\\\\y = \sqrt{36*2}\\\\y = \sqrt{36}*\sqrt{2}\\\\y = 6\sqrt{2}\\\\[/tex]
