Question

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

Explanation:

Step1: Apply Pythagorean theorem

$$a^{2}+b^{2}=c^{2}$$
Let \(a = 2\), \(b = 4\), then \(c^{2}=2^{2}+4^{2}\)

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

$$c^{2}=4 + 16=20$$

Step3: Simplify the radical

$$c=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$$

Answer:

\(2\sqrt{5}\)