Question

find the value of x.

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, assume the two legs are \(6\) and \(8\), and the hypotenuse is \(x\). Then \(6^{2}+8^{2}=x^{2}\).

Step2: Calculate the squares

\(6^{2}=36\) and \(8^{2}=64\). So, \(36 + 64=x^{2}\), which simplifies to \(100=x^{2}\).

Step3: Solve for \(x\)

Taking the square root of both sides, since \(x\) represents the length of a side of a triangle (a non - negative value), \(x=\sqrt{100}=10\).

Answer:

10