Question

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

Explanation:

Step1: Use 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 squares

\(4^{2}=16\), \(6^{2}=36\)
$$16 + 36=c^{2}$$

Step3: Sum the values

\(16+36 = 52\)
$$c^{2}=52$$

Step4: Solve for \(c\)

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

Answer:

\(2\sqrt{13}\)