Question

find the length of the third side. if necessary, write in simplest radical form. answer 1

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to \(a^{2}+b^{2}=c^{2}\) (where \(c = \sqrt{2}\), \(a = 1\), and \(b=x\)), we have \(1^{2}+x^{2}=(\sqrt{2})^{2}\).

Step2: Simplify the equation

\(1 + x^{2}=2\). Then \(x^{2}=2 - 1\). So \(x^{2}=1\).

Step3: Solve for \(x\)

Take the square root of both sides. \(x=\sqrt{1}\). Since \(x>0\) (length of a side), \(x = 1\).

Answer:

\(1\)