Answer:
3 inches, 16 inches, 18 inches
Step-by-step explanation:
we know that
The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side
Verify each case
case 1) we have
5 inches, 8 inches, 20 inches
Applying the triangle Inequality Theorem
1) 5+8 > 20
13 > 20 ------> is not true
therefore
The set of lengths cannot be used to form the sides of a triangle
case 2) we have
3 inches, 16 inches, 18 inches
Applying the triangle Inequality Theorem
1) 3+16 > 18
19 > 18 ------> is true
2) 3+18> 16
21 > 16 -----> is true
3) 16+18 > 3
34 > 3 -----> is true
therefore
The set of lengths can be used to form the sides of a triangle
case 3) we have
2 inches, 5 inches, 7 inches
Applying the triangle Inequality Theorem
1) 2+5 > 7
7 > 7 ------> is not true
therefore
The set of lengths cannot be used to form the sides of a triangle
