The legs of a right triangle are 3 units and 6 units. What is the length of the hypotenuse? Round your answer to the nearest hundredth. (5 points)
5.20 units
6.71 units
9.00 units
18.00 units
To find the length of the hypotenuse, we can use 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 two legs.
Using this theorem, we can calculate the length of the hypotenuse as follows:
hypotenuse^2 = leg1^2 + leg2^2
Substituting the given values:
hypotenuse^2 = 3^2 + 6^2
hypotenuse^2 = 9 + 36
hypotenuse^2 = 45
Taking the square root of both sides to solve for the hypotenuse:
hypotenuse = √45
hypotenuse ≈ 6.71 units
Therefore, the length of the hypotenuse is approximately 6.71 units.
The correct answer is 6.71 units.