Final answer:
To find the hypotenuse of a right triangle with legs measuring 65 cm and 60 cm, we use the Pythagorean theorem: c = √(a² + b²). The calculation yields c = √(65² + 60²) = √(4225 + 3600) = √7825 = 88.43 cm.
Step-by-step explanation:
The question involves finding the length of the hypotenuse of a right triangle when the lengths of the two legs are known, a common application of the Pythagorean theorem. The 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 legs (a and b). In mathematical terms, this is expressed as a² + b² = c².
In this case, one leg (a) measures 65 cm and the other leg (b) measures 60 cm. To find the length of the hypotenuse (c), we use the formula c = √(a² + b²).
Let's calculate:
- a² = 65² = 4225 cm²
- b² = 60² = 3600 cm²
- c² = 4225 cm² + 3600 cm² = 7825 cm²
- c = √7825 cm² = 88.43 cm (rounded to two decimal places)
Therefore, the length of the hypotenuse (c) is approximately 88.43 cm.