Final answer:
In this case, the given triangle with sides 9, 4, and 41 is not a right triangle.
Step-by-step explanation:
A right triangle is a triangle that has one angle measuring 90 degrees. To determine whether the triangle with sides 9, 4, and 41 is a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using the Pythagorean theorem, we can check if the equation a^2 + b^2 = c^2 holds true for the given side lengths. Let's substitute the values:
9^2 + 4^2 = 41^2
81 + 16 = 1681
97 ≠1681
Since 97 is not equal to 1681, we can conclude that the triangle with sides 9, 4, and 41 is not a right triangle.