question\nfind the length of side $x$ in simplest radical form with a rational denominator.\nanswer attempt…

Explanation:

Step1: Identify triangle type

This is an isosceles right triangle (two equal sides, right angle, hypotenuse = 1).

Step2: Apply Pythagorean theorem

For right triangle: $x^2 + x^2 = 1^2$

Step3: Simplify the equation

$2x^2 = 1$

Step4: Solve for $x^2$

$x^2 = \frac{1}{2}$

Step5: Solve for $x$ and rationalize

$x = \sqrt{\frac{1}{2}} = \frac{\sqrt{1}}{\sqrt{2}} = \frac{1 \times \sqrt{2}}{\sqrt{2} \times \sqrt{2}} = \frac{\sqrt{2}}{2}$

Answer:

$\frac{\sqrt{2}}{2}$