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
25, 14, 6	○	○
7, 5, 21	○	○
7.8, 9.6, 16.6	○	○

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 13, 5, 21

$13 + 5=18<21$, so they cannot be side - lengths of a triangle.

Step3: Check 25, 14, 6

$14 + 6 = 20<25$, so they cannot be side - lengths of a triangle.

Step4: Check 7, 5, 21

$7+5 = 12<21$, so they cannot be side - lengths of a triangle.

Step5: Check 7.8, 9.6, 16.6

$7.8+9.6 = 17.4>16.6$, $7.8 + 16.6=24.4>9.6$, $9.6 + 16.6 = 26.2>7.8$, so they can be side - lengths of a triangle.

Answer:

13, 5, 21: Cannot be side lengths of a triangle
25, 14, 6: Cannot be side lengths of a triangle
7, 5, 21: Cannot be side lengths of a triangle
7.8, 9.6, 16.6: Can be side lengths of a triangle