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
7.1, 16.0, 8.4 | ○ | ○
8, 5, 8 | ○ | ○
25, 9, 16 | ○ | ○
2, 9, 14 | ○ | ○

Explanation:

Step1: Recall triangle inequality rule

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

Step2: Test 7.1, 16.0, 8.4

Sort: $7.1, 8.4, 16.0$. Calculate $7.1+8.4=15.5$. $15.5<16.0$, fails rule.

Step3: Test 8, 5, 8

Sort: $5, 8, 8$. Calculate $5+8=13$. $13>8$, passes rule.

Step4: Test 25, 9, 16

Sort: $9, 16, 25$. Calculate $9+16=25$. $25=25$, fails strict inequality.

Step5: Test 2, 9, 14

Sort: $2, 9, 14$. Calculate $2+9=11$. $11<14$, fails rule.

Answer:

Lengths	Can be side lengths of a triangle	Cannot be side lengths of a triangle
8, 5, 8	$\bullet$	$\circ$
25, 9, 16	$\circ$	$\bullet$
2, 9, 14	$\circ$	$\bullet$

(Note: $\bullet$ denotes the selected option)