Kebalikan Teorema Phytagoras Quiz

Explanation
The given answer, 8 cm, 15 cm, and 17 cm, can form a right-angled triangle because it satisfies the Pythagorean theorem, which states that in a right-angled 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 other two sides. In this case, 8^2 + 15^2 = 64 + 225 = 289, which is equal to 17^2. Therefore, these side lengths can form a right-angled triangle.

Explanation
The given answer, 5 cm, 6 cm, and 7 cm, is the correct answer because it does not form a right-angled triangle. In a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. However, in this case, 5^2 + 6^2 is not equal to 7^2, indicating that it is not a right-angled triangle. Therefore, this set of side lengths is the exception and does not form a right-angled triangle.

Explanation
The given answer, (ii) dan (iii), is correct because a triangle is considered acute if all of its angles are less than 90 degrees. In the given options, the lengths of the sides in (ii) and (iii) form triangles with angles less than 90 degrees. However, in options (i) and (iv), at least one of the angles in the triangles formed by the side lengths is equal to or greater than 90 degrees, making them not acute triangles.

Explanation
The given answer states that the triangles with the sizes (ii) 4 cm, 5 cm, and 7 cm and (iv) 4 cm, 8 cm, and 6 cm form obtuse triangles. An obtuse triangle is a triangle that has one angle greater than 90 degrees. To determine if a triangle is obtuse, we can use the Pythagorean theorem. If the sum of the squares of the two shorter sides is less than the square of the longest side, then the triangle is obtuse. By applying this theorem to the given sizes of triangles (ii) and (iv), we can confirm that they form obtuse triangles.

Explanation
The set { 7, 24, 25 } is the only set that satisfies the Pythagorean theorem, which states that in a right-angled 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. In this case, 7^2 + 24^2 = 49 + 576 = 625, which is equal to 25^2. Therefore, the set { 7, 24, 25 } represents the sides of a right-angled triangle.