Question

k 8 10 5 6 7 8

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 10\), \(a = 8\), and \(b=k\). So, \(k^{2}+8^{2}=10^{2}\).

Step2: Simplify the equation

\(k^{2}+64 = 100\). Then, \(k^{2}=100 - 64\).

Step3: Calculate \(k^{2}\)

\(k^{2}=36\).

Step4: Solve for \(k\)

Take the square root of both sides. Since \(k>0\) (length of a side), \(k=\sqrt{36}\).

Answer:

\(6\)