To find the side lengths that make a triangle using the given dimensions, use the first triangle inequality theorem.
The first triangle inequality theorem states that the sum of the lengths of two sides of a triangle must be greater than the length of the third side.
Now, let's check the following:
A. 20 + 21 = 41 is greater than 22
21 + 22 = 43 is greater than 20
20 + 22 = 42 is greater than 21
Therefore, 20, 21, and 22 could make a triangle
B. 80 + 8 = 88 is greater than 80
80 + 80 = 160 is greater than 8
Therefore, 8, 80 and 80 could make a triangle
C. 40 + 50 = 90 is greater than 4
40 + 4 = 44 is less than 50
Therefore, 4, 40 and 50 would not make a triangle.
D. 3 + 3 = 6 is not greater than 6
Therefore, 3, 3 and 6 would not make a triangle
The measures given in Option A and B are correct.
ANSWER:
A. 20, 21 and 22
B. 8, 80 and 80