The figure below is a square. Find the length of side x in simplest radical form with a rational denominator.

Step-by-step explanation:

The diagonal forms two 45-45-90 triangles, with the diagonal being the hypotenuse of both. The Pythagorean Theorem states that , where is the hypotenuse of the triangle, and and are the two legs of the triangle.

From the Isosceles Base Theorem, the two legs of a 45-45-90 triangle are always equal. Since we're given a diagonal of , we have:

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answer for #1 is c

answer for #2 is d

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