Question

sarah has toothpicks that are 4 different lengths, 3 in, 8in, 10in, 11in. she is trying to make as many triangles as she can. how many of the combinations below will make triangles according to the triangle inequality theorem? pick all that apply (3 points) 3,8,10 3,10,11 8,10,11 3,8,11

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 combination 3, 8, 10

$3 + 8=11>10$, $3 + 10 = 13>8$, $8+10 = 18>3$. This combination can form a triangle.

Step3: Check combination 3, 10, 11

$3+10 = 13>11$, $3 + 11=14>10$, $10 + 11=21>3$. This combination can form a triangle.

Step4: Check combination 8, 10, 11

$8 + 10=18>11$, $8 + 11 = 19>10$, $10+11 = 21>8$. This combination can form a triangle.

Step5: Check combination 3, 8, 11

$3+8 = 11$, which is not greater than 11. This combination cannot form a triangle.

Answer:

3, 8, 10; 3, 10, 11; 8, 10, 11