Final answer:
By applying the Pythagorean theorem, we confirmed that a triangle with side lengths 32, 60, and 68 is a right triangle because 32² + 60² equals 68².
Step-by-step explanation:
The question asks whether a triangle with sides of lengths 32, 60, and 68 is a right triangle.
To determine this, we can apply the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs (a and b) is equal to the square of the length of the hypotenuse (c), or a² + b² = c².
Since we are given side lengths of 32, 60, and 68, we need to check whether 32² + 60² equals 68².
Calculating this, we find 32² is 1024, 60² is 3600, and 68² is 4624.
Adding 1024 and 3600 gives us 4624, which is indeed equal to 68².
Therefore, the triangle with these side lengths is indeed a right triangle.