Final answer:
In a right triangle with side lengths of 6cm, 8cm, and 10cm, the hypotenuse is the longest side, which measures 10cm, as determined by applying the Pythagorean theorem.
Step-by-step explanation:
The student has asked which length is that of the hypotenuse in a right triangle with sides of 6cm, 8cm, and 10cm. According to the Pythagorean theorem, which 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), given by the formula c = √(a² + b²).
By applying the Pythagorean theorem:
- a² + b² = c²
- 6² + 8² = c²
- 36 + 64 = c²
- 100 = c²
- c = √100
- c = 10cm
Therefore, the hypotenuse of this right triangle is the longest side, which is 10cm.