A right triangle has leg lengths that are 5 meters and 6 meters, respectively. Which of the following lengths, in meters, is closest to that of the hypotenuse of the right triangle?
√ ( 5² + 6² ) = √ ( 25 + 36 ) = √ 61 = 7.8102496759
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean Theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's denote the length of the two legs as 'a' and 'b', and the length of the hypotenuse as 'c'. According to the Pythagorean Theorem:
c^2 = a^2 + b^2
In this case, one leg has a length of 5 meters and the other leg has a length of 6 meters. Let's calculate the length of the hypotenuse:
c^2 = (5^2) + (6^2)
c^2 = 25 + 36
c^2 = 61
To find the length of the hypotenuse 'c', we take the square root of both sides:
c = √61
Now, let's find which of the given lengths is closest to √61:
-√61 is approximately -7.81
√61 is approximately 7.81
10 is approximately 10.00
11 is approximately 11.00
15 is approximately 15.00
Since the question asks for the length closest to the hypotenuse, we can see that 10 meters is the closest length to √61.