The lengths of the legs of a right triangle are 6 inches and 8 inches. What is the length of the hypotenuse?
We can use the Pythagorean theorem to find the length of the hypotenuse. The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let c be the length of the hypotenuse.
According to the Pythagorean theorem, we have:
c^2 = a^2 + b^2
where a and b are the lengths of the legs of the right triangle.
Substituting a = 6 inches and b = 8 inches, we have:
c^2 = 6^2 + 8^2
= 36 + 64
= 100
Taking the square root of both sides, we have:
c = √100
= 10
Therefore, the length of the hypotenuse is 10 inches.
To find the length of the hypotenuse of a right triangle, you can use the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two legs.
Step 1: Determine the squares of the lengths of each leg.
- The square of the length of the first leg is 6^2 = 36.
- The square of the length of the second leg is 8^2 = 64.
Step 2: Add the squares of the two legs.
36 + 64 = 100
Step 3: Take the square root of the sum to find the length of the hypotenuse.
The square root of 100 is 10.
Therefore, the length of the hypotenuse of the right triangle is 10 inches.