A triangle has sides with lengths of 41 yards, 50 yards, and 65 yards. 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 a² + b² = c².

In this case, the sides of the triangle are 41 yards, 50 yards, and 65 yards. If this is a right triangle, the 65-yard side should be the hypotenuse, as it is the longest side.

Let's check the equation:

41² + 50² = 65² 1681 + 2500 = 4225 4181 = 4225

Since 4181 does not equal 4225, this triangle is not a right triangle.