Question

find the length of the third side. if necessary, write in simplest radical form.
answer
attempt 1 out of 3

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 1\) and \(b = 1\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\). Substitute \(a = 1\) and \(b = 1\) into the formula: \(c^{2}=1^{2}+1^{2}\).

Step2: Calculate \(c^{2}\)

\(c^{2}=1 + 1=2\).

Step3: Solve for \(c\)

Take the square root of both sides. Since \(c>0\) (length of a side of a triangle), \(c=\sqrt{2}\).

Answer:

\(\sqrt{2}\)