Question

what is the value of x in the diagram below?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). Here, \(a = 6\), \(c = 10\), and \(b=x\). So, \(x^{2}+6^{2}=10^{2}\).

Step2: Simplify the equation

\(x^{2}+36 = 100\). Then, \(x^{2}=100 - 36\).

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

\(x^{2}=64\).

Step4: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle (\(x>0\)), \(x=\sqrt{64}\).

Answer:

\(8\)