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
29, 18, 7 | ○ | ○
4.2, 11.2, 7.9 | ○ | ○
8, 10, 9 | ○ | ○
5, 4, 12 | ○ | ○

Explanation:

Step1: Recall triangle inequality rule

For lengths $a,b,c$ (sorted $a\leq b\leq c$), check $a+b > c$.

Step2: Test 29, 18, 7

Sort: $7,18,29$. Calculate $7+18=25$. $25 < 29$

Step3: Test 4.2, 11.2, 7.9

Sort: $4.2,7.9,11.2$. Calculate $4.2+7.9=12.1$. $12.1 > 11.2$

Step4: Test 8, 10, 9

Sort: $8,9,10$. Calculate $8+9=17$. $17 > 10$

Step5: Test 5, 4, 12

Sort: $4,5,12$. Calculate $4+5=9$. $9 < 12$

Answer:

Lengths	Can be side lengths of a triangle	Cannot be side lengths of a triangle
4.2, 11.2, 7.9	$\bigcirc$
8, 10, 9	$\bigcirc$
5, 4, 12		$\bigcirc$