A triangle has sides with lengths of 32 yards, 60 yards, and 68 yards. Is it a right triangle?

To determine if a triangle is a right triangle, we can use the Pythagorean theorem. The theorem 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 can be written as: a² + b² = c².

In this case, the sides of the triangle are 32 yards, 60 yards, and 68 yards. If this is a right triangle, 68 yards would be the hypotenuse, as it is the longest side. So, we can set up the equation as follows:

32² + 60² = 68² 1024 + 3600 = 4624

Adding 1024 and 3600 gives 4624, which is indeed equal to 4624. Therefore, the triangle with sides of 32 yards, 60 yards, and 68 yards is a right triangle.