Question

select all of the sets of side lengths that will form a triangle. *
□ 30, 40, 50
□ 11, 22, 33
□ 40, 41, 80
□ 33, 44, 88
□ 100, 199, 298

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 30, 40, 50

$30 + 40=70>50$, $30 + 50 = 80>40$, $40+50 = 90>30$. So, it can form a triangle.

Step3: Check 11, 22, 33

$11 + 22=33$, which is not greater than 33. So, it cannot form a triangle.

Step4: Check 40, 41, 80

$40+41 = 81>80$, $40 + 80=120>41$, $41+80 = 121>40$. So, it can form a triangle.

Step5: Check 33, 44, 88

$33+44 = 77<88$. So, it cannot form a triangle.

Step6: Check 100, 199, 298

$100+199 = 299>298$, $100 + 298=398>199$, $199+298 = 497>100$. So, it can form a triangle.

Answer:

30, 40, 50; 40, 41, 80; 100, 199, 298