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Sagot :
Answer:
• 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:
[tex]\begin{gathered} a+b>c \\ a+c>b \\ b+c>a \end{gathered}[/tex]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)
[tex]\begin{gathered} 3+4=7<8 \\ 3+8=11>4 \\ 4+8=12>3 \end{gathered}[/tex]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)
[tex]\begin{gathered} 7+6=13>12 \\ 7+12=19>13 \\ 6+12=18>7 \end{gathered}[/tex]The triangle inequality holds, thus, 7 units, 6 units, and 12 units make a triangle.
Option 3 (5,13 and 11)
[tex]\begin{gathered} 5+13=18>11 \\ 5+11=16>13 \\ 13+11=24>5 \end{gathered}[/tex]The triangle inequality holds, thus, 5 units, 13 units, and 11 units make a triangle.
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