A triangle has sides with lengths of 16 kilometers, 66 kilometers, and 67 kilometers. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right 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 is often written as a^2 + b^2 = c^2.

In this case, we can consider the side with length 67 kilometers as the hypotenuse, since it is the longest side. The other two sides have lengths of 16 kilometers and 66 kilometers.

So, we can plug these values into the Pythagorean theorem:

(16 km)^2 + (66 km)^2 = (67 km)^2

256 km^2 + 4356 km^2 = 4489 km^2

4612 km^2 = 4489 km^2

Since the two sides of the equation are not equal, the triangle is not a right triangle.