Question

find the value of x.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 6\) and \(b = 8\) and hypotenuse \(x\), the Pythagorean theorem is \(a^{2}+b^{2}=x^{2}\). So \(6^{2}+8^{2}=x^{2}\).

Step2: Calculate the squares

\(6^{2}=36\) and \(8^{2}=64\). Then \(36 + 64=x^{2}\), so \(x^{2}=100\).

Step3: Solve for \(x\)

Taking the square - root of both sides, \(x=\sqrt{100}\). Since \(x\) represents the length of a side of a triangle, \(x = 10\) (we take the positive square root as length cannot be negative).

Answer:

10