MHB Right Isosceles triangle: solve for the length of the unknown legs

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In a right isosceles triangle with a hypotenuse of length 1, the lengths of the legs can be found using the Pythagorean theorem. Setting the length of each leg as "x," the equation becomes x² + x² = 1², simplifying to 2x² = 1. Solving for x gives x² = 1/2, leading to x = √(1/2). Rationalizing the denominator results in x = √2/2. Thus, the length of each leg in the triangle is √2/2.
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For a right isosceles triangle (45-45-90) of hypotenuse 1, solve for the length of the unknown legs. Give an exact answer and rationalize the denominator in the final answer.
 
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Call the length of each leg "x" and set up the Pythagorean theorem. Solve for x.
 

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