Calculate the hypotenuse of a right triangle with legs measuring 6 cm and 8 cm.

To calculate the hypotenuse of a right triangle when the lengths of the two legs are known, you can utilize 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 lengths of the legs are given as 6 cm and 8 cm. According to the Pythagorean theorem, the relationship can be expressed as:

[ c^2 = a^2 + b^2 ]

Substituting the values of the legs into this equation:

[ c^2 = 6^2 + 8^2 ]

[ c^2 = 36 + 64 ]

[ c^2 = 100 ]

Next, to find the length of the hypotenuse (c), we take the square root of 100:

[ c = \sqrt{100} = 10 \text{ cm} ]

Therefore, the hypotenuse of the triangle measures 10 cm. This calculation correctly identifies that the distance across from one leg to the other (the hypotenuse) is the