Question

for each set of three lengths, determine if they can be the side lengths of a triangle.

lengths	can be side lengths of a triangle	cannot be side lengths of a triangle
21.2, 3.7, 16.8	○	○
6, 3, 6	○	○
18, 6, 12	○	○

Explanation:

Step1: Recall triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Step2: Check 17, 4, 9

$4 + 9=13<17$, so they cannot be side - lengths of a triangle.

Step3: Check 21.2, 3.7, 16.8

$3.7+16.8 = 20.5<21.2$, so they cannot be side - lengths of a triangle.

Step4: Check 6, 3, 6

$3 + 6=9>6$, $6 + 6 = 12>3$, $6+3 = 9>6$, so they can be side - lengths of a triangle.

Step5: Check 18, 6, 12

$6 + 12=18$, which does not satisfy the triangle - inequality theorem, so they cannot be side - lengths of a triangle.

Answer:

Lengths	Can be side lengths of a triangle	Cannot be side lengths of a triangle
21.2, 3.7, 16.8		$\bigcirc$
6, 3, 6	$\bigcirc$
18, 6, 12		$\bigcirc$