Final answer:
There can only be one triangle with side lengths of 7 cm, 4 cm, and 5 cm since any permutation of these sides would still form the same triangle.
The triangle is not right-angled, as determined by the Pythagorean theorem, since the squares of the sides do not sum to the square of the largest side (7 cm).
Step-by-step explanation:
A triangle with side lengths of 7 cm, 4 cm, and 5 cm is unique given the fact that the sum of any two sides must be greater than the third for a valid triangle.
This condition is satisfied by the given measurements. Whether this triangle is a right triangle can be determined by the Pythagorean theorem, which states that for 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.
The Pythagorean theorem is defined as a² + b² = c², where c represents the length of the hypotenuse, and a and b are the lengths of the other two sides of the triangle.
In this case, if we apply the theorem to check if the triangle is right-angled, we get 4² + 5² = 16 + 25 = 41, which does not equal 7² or 49. Therefore, the triangle with sides of 7 cm, 4 cm, and 5 cm is not a right triangle.
Since the order of the sides does not change the shape of the triangle, there is only one triangle that can be made with these specific measurements. Thus, the triangle with side lengths of 7 cm, 4 cm, and 5 cm is unique.