Final answer:
The given triangle with sides of 25 km, 46 km, and 54 km is not a right triangle, as its side lengths do not satisfy the Pythagorean theorem, which states a² + b² = c² for the sides of a right triangle.
Step-by-step explanation:
Whether a triangle with sides of lengths 25 kilometers, 46 kilometers, and 54 kilometers is a right triangle can be determined by applying the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed in the formula a² + b² = c².
To test the given side lengths, we need to identify the longest side to act as the hypotenuse, which in this case is the side of length 54 kilometers. We then need to square each of the side lengths and check the equation: 25² + 46² = 54², or, 625 + 2116 = 2916.
After calculating, we find that 625 + 2116 equals 2741, which does not equal 2916. Since the sum of the squares of the two shorter sides does not equal the square of the longest side, we can conclude that this triangle is not a right triangle.