Question

find the missing side

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 5\) and \(b = 6\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\). So \(x^{2}=5^{2}+6^{2}\).

Step2: Calculate squares

\(5^{2}=25\) and \(6^{2}=36\), then \(x^{2}=25 + 36=61\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, \(x=\sqrt{61}\).

Answer:

\(\sqrt{61}\)