Final answer:
A triangle with side lengths of 5m, 7m, and 9m does not satisfy the Pythagorean theorem and so is not right-angled. Since all sides are of different lengths, it is classified as a scalene triangle.
Step-by-step explanation:
To classify a triangle with side lengths of 5m, 7m, and 9m, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In formula form, this is c² = a² + b² where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
Applying this to our triangle, the longest side, which would be the hypotenuse if this were a right triangle, is 9m. We thus calculate 9² = 81. Then we take the sum of the squares of the other two sides: 5² + 7² = 25 + 49 = 74. Since 81 is greater than 74, the sides do not satisfy the Pythagorean theorem, meaning this is not a right-angled triangle.
Since all sides have different lengths, this triangle is scalene. Therefore, the triangle with side lengths of 5m, 7m, and 9m is classified as a scalene triangle.