In a right triangle, one leg measures $6$ units, the other leg measures $8$ units, and the hypotenuse is labeled $x$. What is the value of $x$?

• A. $10$
• B. $7$
• C. $14$
• D. $12$

Answer: (A)

Verified step by step guidance

1. Identify the sides of the right triangle: the two legs are given as 6 units and 8 units, and the hypotenuse is labeled as \(x\).
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the legs: \(x^2 = a^2 + b^2\).
3. Substitute the known leg lengths into the Pythagorean theorem: \(x^2 = 6^2 + 8^2\).
4. Calculate the squares of the legs: \$6^2 = 36\( and \)8^2 = 64\(, so the equation becomes \)x^2 = 36 + 64$.
5. Add the values on the right side and then take the square root of both sides to solve for \(x\): \(x = \sqrt{36 + 64}\).