A triangle has sides with lengths of 3 meters, 5 meters, and 6 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 6 meters.

Step 2: Apply the Pythagorean theorem. Square the lengths of the two shorter sides and add them together. Then square the length of the longest side.

(3^2) + (5^2) = 9 + 25 = 34

(6^2) = 36

Step 3: Compare the results. If the sum of the squares of the two shorter sides is equal to the square of the longest side, then the triangle is a right triangle.

In this case, 34 is not equal to 36, so the triangle is not a right triangle.