Final answer:
Using the Pythagorean theorem, the hypotenuse of a right triangle with legs measuring 5cm and 6cm is found to be √61 cm when left in exact solution form.
Step-by-step explanation:
The student asked about the length of the hypotenuse in a right triangle with legs measuring 5cm and 6cm. To solve this, we use 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).
Using the theorem:
- a² + b² = c²
- 5cm² + 6cm² = c²
- 25cm² + 36cm² = c²
- 61cm² = c²
- c = √61cm²
- c = √61 cm
Therefore, the length of the hypotenuse in exact solution form is √61 cm.