In the right triangle shown, the length of $a$ is $6$ units and the length of $b$ is $8$ units. What is the length of the hypotenuse $c$?

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

Answer: (D)

Verified step by step guidance

1. Identify the sides of the right triangle: sides \(a = 6\) units and \(b = 8\) units are the legs, and \(c\) is the hypotenuse, which is the side opposite the right angle.
2. Recall the Pythagorean theorem, which relates the sides of a right triangle: \(c^2 = a^2 + b^2\). This formula allows us to find the hypotenuse when the legs are known.
3. Substitute the known values into the Pythagorean theorem: \(c^2 = 6^2 + 8^2\).
4. Calculate the squares of the legs: \(6^2 = 36\) and \(8^2 = 64\), then add them to get \(c^2 = 36 + 64\).
5. Take the square root of both sides to solve for \(c\): \(c = \sqrt{36 + 64}\). This will give the length of the hypotenuse.