Final answer:
A Pythagorean triplet is not formed by the numbers 5, 10, and 12, but a triangle with sides measuring 6 cm, 8 cm, and 10 cm is a right-angled triangle.
Step-by-step explanation:
A Pythagorean triplet is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2. To check if the triplet 5, 10, 12 is a Pythagorean triplet, we can square the values of the numbers and check if the sum of the squares of the two smaller numbers is equal to the square of the largest number. In this case, 5^2 + 10^2 = 25 + 100 = 125, which is not equal to 12^2 = 144. Therefore, the triplet 5, 10, 12 is not a Pythagorean triplet.
To check if a triangle with sides measuring 6 cm, 8 cm, and 10 cm is a right-angled triangle, we can use the Pythagorean theorem. According to the theorem, 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. Here, 6^2 + 8^2 = 36 + 64 = 100, which is equal to 10^2. Hence, the triangle with sides measuring 6 cm, 8 cm, and 10 cm is a right-angled triangle.
Learn more about Pythagorean triplet and right-angled triangle