Question

Select ALL the sets of side lengths that will make a triangle O 3 units, 4 units, 8 units 0 7 units, 6 units, 12 units O 5 units, 13 units, 11 units o 4 units, 6 units, 10 units

Answer 1

• 7 units, 6 units, 12 units

,

• 5 units, 13 units, 11 units

,

•

Explanation:

Given three side lengths, a, b, and c. To determine if they will make a triangle, we check if they satisfy the triangle inequality given below:

`\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}`

What this means is that for the side lengths to form a triangle, "the sum of any two sides must be greater than the third side".

We test the values below:

Option 1 (3,4 and 8)

`\begin{gathered} 3+4=7<8 \\ 3+8=11>4 \\ 4+8=12>3 \end{gathered}`

In the first case, 7 is not greater than 8, does, the triangle inequality does not hold, and thus, 3 units, 4 units, 8 units do not make a triangle.

Option 2 (7,6 and 12)

`\begin{gathered} 7+6=13>12 \\ 7+12=19>13 \\ 6+12=18>7 \end{gathered}`

The triangle inequality holds, thus, 7 units, 6 units, and 12 units make a triangle.

Option 3 (5,13 and 11)

`\begin{gathered} 5+13=18>11 \\ 5+11=16>13 \\ 13+11=24>5 \end{gathered}`

The triangle inequality holds, thus, 5 units, 13 units, and 11 units make a triangle.