Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - angled triangle, the Pythagorean theorem states that \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs of the right - triangle and \(c\) is the hypotenuse. In this isosceles right - triangle (since the two legs are equal, as indicated by the tick marks), \(a = b=\sqrt{11}\). So, \(x^{2}=(\sqrt{11})^{2}+(\sqrt{11})^{2}\).

Step2: Simplify the equation

First, calculate \((\sqrt{11})^{2}=11\). Then \(x^{2}=11 + 11\). So, \(x^{2}=22\).

Step3: Solve for \(x\)

Take the square root of both sides. \(x=\sqrt{22}\).

Answer:

\(\sqrt{22}\)