Question

find the exact length of the missing side of the right triangle.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(a = 4\), \(b = 6\).
$$4^{2}+6^{2}=c^{2}$$

Step2: Calculate \(4^{2}\) and \(6^{2}\)

\(4^{2}=16\), \(6^{2}=36\). Then \(16 + 36=c^{2}\), so \(c^{2}=52\).

Step3: Find \(c\)

\(c=\sqrt{52}\), simplify \(\sqrt{52}=\sqrt{4\times13}=2\sqrt{13}\).

Answer:

\(2\sqrt{13}\)