find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 2 x =

Explanation:

Step1: Identify the triangle type

This is a 45 - 45 - 90 right - triangle. In a 45 - 45 - 90 triangle, the ratio of the sides is $1:1:\sqrt{2}$, where the hypotenuse is $\sqrt{2}$ times the length of each leg. Let the length of each leg be $x$ and the hypotenuse be $c = 1$.

Step2: Apply the ratio formula

We know that $c=\sqrt{2}x$. Given $c = 1$, we can solve for $x$ by the equation $1=\sqrt{2}x$.

Step3: Solve for $x$

$x=\frac{1}{\sqrt{2}}$. To rationalize the denominator, we multiply the numerator and denominator by $\sqrt{2}$. So $x=\frac{1\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}=\frac{\sqrt{2}}{2}$.

Answer:

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