Answer:
The group of line segments that could form the other 2 sides of the triangle is;
B. 7 cm and 8 cm
Step-by-step explanation:
The triangle inequality theorem states that the sum of the length of any two sides of a triangle is larger than the length of the third side
The given parameter of the triangle is that the length of the longest side of the triangle = 10 cm
Let, 'a', and 'b', represent the remaining two sides of the triangle
Therefore, by the triangle inequality theorem, we have;
(1) a + b > 10 cm
(2) 10 cm + a > b
(3) 10 cm + b > a
The option that satisfies condition (1), (2), and (3) are options 'B' and 'D', for which we have;
7 cm + 8 cm = 15 cm > 10 cm
10 cm + 7 cm = 17 cm > 8 cm
10 cm + 8 cm = 18 cm > 7 cm
9 cm + 10 cm = 19 cm > 10 cm
10 cm + 9 cm = 19 cm > 10 cm
10 cm + 10 cm = 20 cm > 9 cm
Therefore, the possible combination of the other two sides are;
7 cm and 8 cm or 9 cm and 10 cm
However, a side of option 'D' is 10 cm and given that the longest side of the triangle = 10 cm, the length of each of the other two side should be less than 10 cm and the only given possible combination of the other two side should be option 'B', 7 cm and 8 cm.
