Final answer:
Using the Pythagorean theorem, the length of the hypotenuse in a 45°-45°-90° triangle with 12 cm legs is calculated as 12√2 cm, which is approximately 16.97 cm.
Step-by-step explanation:
The student's question asks about the length of the hypotenuse in a 45°-45°-90° triangle where each leg measures 12 cm. To solve for the hypotenuse, Pythagorean theorem is applied, which states that in a right-angled 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). Since it's a 45°-45°-90° triangle, both legs are equal in length, so we can denote each as 'a'.
The Pythagorean theorem is given as:
a² + a² = c²
This simplifies to:
2a² = c²
c = √(2 × a²)
By substituting the length of a leg (12 cm):
c = √(2 × 12²)
c = √(2 × 144)
c = √(288)
c = 12√2 cm
Thus, the hypotenuse is 12√2 cm, which is approximately 16.97 cm.