Final answer:
A triangle with side lengths 9 mm, 40 mm, and 41 mm is a right triangle, as it satisfies the Pythagorean theorem where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Step-by-step explanation:
To determine if a triangle with sides of lengths 9 millimeters, 40 millimeters, and 41 millimeters is a right triangle, we can use the Pythagorean theorem. This 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.
Let's label the sides as follows: side a is 9 mm, side b is 40 mm, and side c, the potential hypotenuse, is 41 mm. According to the Pythagorean theorem, a right triangle must satisfy the equation a² + b² = c².
Plugging in the values, we get:
Since both sides of the equation are equal, we can confirm that the triangle is indeed a right triangle. Thus, a triangle with sides 9 mm, 40 mm, and 41 mm forms a right angle between the sides measuring 9 mm and 40 mm, with the 41 mm side as the hypotenuse.