Question

find the length of the third side. if necessary, write in simplest radical form.
answer attempt 1 out of 2
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Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 8\), \(b = 8\), and \(c\) is the hypotenuse (the third side).
$$8^{2}+8^{2}=c^{2}$$

Step2: Calculate the sum of squares

\(8^{2}=64\), so \(64 + 64=c^{2}\), which means \(c^{2}=128\).

Step3: Simplify the radical

\(c=\sqrt{128}=\sqrt{64\times2}\). Since \(\sqrt{ab}=\sqrt{a}\times\sqrt{b}\) (\(a = 64\geq0\), \(b = 2\geq0\)), then \(c = \sqrt{64}\times\sqrt{2}=8\sqrt{2}\).

Answer:

\(8\sqrt{2}\)