Question

find the length of side x in simplest radical form with a rational denominator. answer attempt 1 out of 3 x =

Explanation:

Step1: Identify 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 legs are of equal length and the hypotenuse $c$ is related to a leg $a$ by $c = a\sqrt{2}$. Here, a leg has length $a = 9$.

Step2: Calculate hypotenuse length

Using the formula $c=a\sqrt{2}$, substituting $a = 9$, we get $x=9\sqrt{2}$. Since the denominator is already rational (in the non - fraction sense as there is no fraction with an irrational denominator in the form we have), this is the simplest form with a rational denominator.

Answer:

$9\sqrt{2}$