In a right triangle, one leg has length $6$ and the hypotenuse has length $10$. Find the length of the other leg $x$ in simplest radical form with a rational denominator.

• A. $8$
• B. $\frac{8}{1}$
• C. $\frac{2}{1}\sqrt{19}$
• D. $4\sqrt{7}$

Answer: (A)

Verified step by step guidance

1. Identify the given elements in the right triangle: one leg length is 6, the hypotenuse length is 10, and the other leg length is unknown, denoted as \(x\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the legs equals the square of the hypotenuse: \(a^2 + b^2 = c^2\).
3. Substitute the known values into the Pythagorean theorem: \$6^2 + x^2 = 10^2$.
4. Simplify the squares: \$36 + x^2 = 100$.
5. Isolate \(x^2\) by subtracting 36 from both sides: \(x^2 = 100 - 36\), then take the square root of both sides to find \(x\) in simplest radical form, ensuring the denominator is rational.