A right triangle has legs of 6 units and 8 units. What is the length of the hypotenuse?

To find the length of the hypotenuse in a right triangle when the lengths of the legs are known, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, the legs of the triangle are 6 units and 8 units. Applying the Pythagorean theorem:

c² = a² + b²

c² = 6² + 8²

c² = 36 + 64

c² = 100

To find the hypotenuse (c), take the square root of both sides:

c = √100

c = 10

Therefore, the length of the hypotenuse is 10 units. The correct response identifies the hypotenuse as 10, which aligns with the calculations based on the Pythagorean theorem. The other provided choices either restate 10 in different formats or suggest incorrect numerical relationships, but they do not affect the determination of the hypotenuse's correct length.