Question

find the length of the third side. if necessary, write in simplest radical form. answer attempt 2 out of 2 2 2

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate \(a^{2}+b^{2}\)

\(2^{2}=4\), so \(2^{2}+2^{2}=4 + 4=8\). Then \(c^{2}=8\).

Step3: Solve for \(c\)

Take the square root of both sides: \(c=\sqrt{8}\).
Simplify \(\sqrt{8}=\sqrt{4\times2}\).
Since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 4\), \(b = 2\)), \(\sqrt{4\times2}=\sqrt{4}\times\sqrt{2}\).
And \(\sqrt{4}=2\), so \(c = 2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)