Question

select all the sets of side lengths that make a triangle. not quite, keep trying. (select all that apply.) 3, 3, 5 9, 12, 20 10, 10, 10 14, 15, 30 6, 6, 16 8, 15, 25

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 3, 3, 5

$3 + 3=6>5$, $3 + 5 = 8>3$, $5+3 = 8>3$. So, 3, 3, 5 can form a triangle.

Step3: Check 9, 12, 20

$9 + 12=21>20$, $9 + 20 = 29>12$, $12+20 = 32>9$. So, 9, 12, 20 can form a triangle.

Step4: Check 10, 10, 10

$10 + 10=20>10$, $10 + 10 = 20>10$, $10+10 = 20>10$. So, 10, 10, 10 can form a triangle.

Step5: Check 14, 15, 30

$14 + 15=29<30$. So, 14, 15, 30 cannot form a triangle.

Step6: Check 6, 6, 16

$6 + 6=12<16$. So, 6, 6, 16 cannot form a triangle.

Step7: Check 8, 15, 25

$8 + 15=23<25$. So, 8, 15, 25 cannot form a triangle.

Answer:

3, 3, 5; 9, 12, 20; 10, 10, 10