Final answer:
Yes, the triangle with sides measuring 9 km, 12 km, and 15 km is a right triangle.
Step-by-step explanation:
A triangle with sides measuring 9 kilometers, 12 kilometers, and 15 kilometers can be determined to be a right triangle or not using the Pythagorean theorem.
The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's check if this holds true for the given triangle:
Square the lengths of the two shorter sides: (9 km)2 = 81 km2 and (12 km)2 = 144 km2
Add the squared lengths of the two shorter sides: 81 km2 + 144 km2 = 225 km2
Take the square root of the sum: √(225 km2) = 15 km
Since the square of the length of the hypotenuse (15 km) is equal to the sum of the squares of the lengths of the other two sides (81 km2 + 144 km2 = 225 km2), the given triangle is a right triangle.
Therefore, the answer to the question is yes, it is a right triangle.