In a right triangle, if one leg has length $a$ = $6$, the other leg has length $b$ = $8$, and the hypotenuse is $x$, what is the value of $x$?

• A. $10$
• B. $12$
• C. $8$
• D. $14$

Answer: (A)

Verified step by step guidance

1. Identify that the triangle is a right triangle with legs of lengths \(a = 6\) and \(b = 8\), and hypotenuse \(x\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs: \(x^2 = a^2 + b^2\).
3. Substitute the given values into the Pythagorean theorem: \(x^2 = 6^2 + 8^2\).
4. Calculate the squares of the legs: \$6^2 = 36\( and \)8^2 = 64\(, so \)x^2 = 36 + 64$.
5. Add the values to get \(x^2 = 100\), then take the square root of both sides to find \(x = \sqrt{100}\).