A triangle has sides with lengths of 12 millimeters, 35 millimeters, and 37 millimeters. 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, if the triangle is a right triangle, then 37 millimeters would be the length of the hypotenuse (since it is the longest side), and 12 millimeters and 35 millimeters would be the lengths of the other two sides.

So, we can check if 12^2 + 35^2 = 37^2.

12^2 = 144 35^2 = 1225 37^2 = 1369

Adding 144 and 1225 gives us 1369, which is equal to 37^2.

So, yes, the triangle is a right triangle.