A triangle has sides with lengths of 40 meters, 75 meters, and 85 meters. 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.

Step 1: Identify the longest side. In this case, the longest side is 85 meters.

Step 2: Square the lengths of all sides: 40^2 = 1600 75^2 = 5625 85^2 = 7225

Step 3: Check if the square of the longest side is equal to the sum of the squares of the other two sides: 1600 + 5625 = 7225

Since 7225 = 7225, the triangle is a right triangle.