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

D. 4 centimeters, 6 centimeters, 9 centimeters

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`