Question

is it a triangle
you have 8 cards in this activity.
0 are sorted correctly.
possible side lengths for triangle
not possible side lengths for triangle
42, 38, 5
5, 5, 5
9, 11, 3
2, 12, 15
3, 3, 6
37, 11, 20

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 side - lengths 42, 38, 5

$38 + 5=43>42$, $42 + 5 = 47>38$, $42+38 = 80>5$. So, it can form a triangle.

Step3: Check side - lengths 9, 11, 3

$9 + 3=12>11$, $11 + 3 = 14>9$, $9+11 = 20>3$. So, it can form a triangle.

Step4: Check side - lengths 5, 5, 5

Since $5 + 5=10>5$, it is an equilateral triangle.

Step5: Check side - lengths 2, 12, 15

$2+12 = 14<15$. So, it cannot form a triangle.

Step6: Check side - lengths 3, 3, 6

$3 + 3=6$. According to the triangle - inequality theorem, the sum must be strictly greater, so it cannot form a triangle.

Step7: Check side - lengths 37, 11, 20

$11 + 20=31<37$. So, it cannot form a triangle.

Answer:

Possible Side Lengths for Triangle: 42, 38, 5; 9, 11, 3; 5, 5, 5
Not Possible Side Lengths for Triangle: 2, 12, 15; 3, 3, 6; 37, 11, 20