Question

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 \(a = 2\), \(b=\sqrt{5}\) and hypotenuse \(c\), the Pythagorean theorem is \(c^{2}=a^{2}+b^{2}\).
Substitute \(a = 2\) and \(b=\sqrt{5}\) into the formula: \(c^{2}=2^{2}+(\sqrt{5})^{2}\).

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

\(2^{2}=4\) and \((\sqrt{5})^{2}=5\). Then \(c^{2}=4 + 5\).

Step3: Solve for \(c\)

\(c^{2}=9\), so \(c=\sqrt{9}=3\).

Answer:

\(3\)