A triangle has sides with lengths of 30 centimeters, 35 centimeters, and 45 centimeters. 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, the 45 cm side would be the hypotenuse, since it is the longest side. So, we can check the equation:

30^2 + 35^2 = 45^2 900 + 1225 = 2025 2125 = 2025

Since 2125 is not equal to 2025, the triangle is not a right triangle.