Final answer:
The side lengths of 14, 50, and 48 satisfy the Pythagorean Theorem because the sum of the squares of the shorter sides (196 + 2304) equals the square of the longest side (2500), thus confirming they can form a right triangle.
Step-by-step explanation:
The question asks whether the side lengths of 14, 50, and 48 satisfy the Pythagorean Theorem, which relates to the lengths of the sides of a right triangle. To determine if these lengths form a right triangle, we calculate whether the sum of the squares of the two shorter sides (14 and 48) is equal to the square of the longest side (50), according to the theorem's formula a² + b² = c².
Let's plug in the numbers and check:
- 14² = 196
- 48² = 2304
- 50² = 2500
Now, we add the squares of the shorter sides:
196 + 2304 = 2500
Since the sum of the squares of the legs (14 and 48) equals the square of the hypotenuse (50), we can confirm that these side lengths do indeed satisfy the Pythagorean Theorem and can form a right triangle.