Answer:
4) i) The numbers can represent the side lengths of a triangle
ii) Right triangle
5) i) The numbers can represent the side lengths of a triangle
ii) Isosceles triangle
6) i) The numbers can represent the lengths of the sides of a triangle
ii) Pythagoras theorem
7) The numbers do not represent the lengths of sides of a triangle
8) i) The numbers can represent the side lengths of a triangle
ii) Scalene triangle
Explanation:
In a triangle, the sum of the lengths of the two shorter sides is longer than the length of the longest side
The given numbers are;
4) i) 15, 20, 25
Given that 15 + 20 < 25, the numbers can represent the side lengths of a triangle
ii) 15² + 20² = 25²
Therefore, the sides lengths are in line with the side length of a right triangle as their relation is given by Pythagoras theorem
The triangle is a right triangle
5) i) The given numbers are;
2, 6, 6
Given that 2 + 6 > 6, the numbers can represent the side lengths of a triangle
ii) Given that the lengths of two sides are equal (6 each), the triangle formed by the numbers is an isosceles triangle
6) i) 0.27, 0.36, 0.45
0.27 + 0.36 = 0.63 > 0.45, therefore, the numbers can represent the lengths of the sides of a triangle
ii) Given that 0.27² + 0.36² = 0.45², according to Pythagoras theorem, the type of triangle formed is a right triangle
7) 2.5, 1.5, 4
Given that 2.5 + 1.5 = 4, the numbers do not meet the criteria for forming triangles and therefore they cannot represent the side lengths of a triangle
8) i) 12, 16, 25
12 + 16 = 28 > 25, the numbers can represent the side lengths of a triangle
ii) 12² + 16² = 400 < 25² = 625, therefore, the triangle formed by the numbers is not a right triangle but a scalene triangle.