Question

Which sets of side lengths could form a triangle?
A. 3 centimeters, 4 centimeters, 9 centimeters
B. 3 centimeters, 6 centimeters, 9 centimeters
C. 4 centimeters, 5 centimeters, 9 centimeters
D. 4 centimeters, 6 centimeters, 9 centimeters

Answer 1

Answer:

D. 4 centimeters, 6 centimeters, 9 centimeters

Step-by-step explanation:

Considering side length for forming a triangle, most of the time it is about Triangle Inequality Theorem, which for 3 sides length a,b,c, it must satisfy the following set of inequalities:  

$a+b>c\\a+c>b\\b+c>a$

By checking each of them only D satisfy:

$4+6=10>9\\6+9=15>4\\9+4=13>6$

For simplicity you only have to check if the two shortest sides add up to be larger than the longest side:

$4+6>9$