Question

for each set of three lengths, determine if they can be the side lengths of a triangle. lengths can be side lengths of a triangle cannot be side lengths of a triangle 4, 11, 9 15, 7, 18 9, 8, 10 7.8, 8.4, 16.2

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 4, 11, 9

$4 + 9=13>11$, $4 + 11 = 15>9$, $9+11 = 20>4$. So, it can be side - lengths of a triangle.

Step3: Check 15, 7, 18

$15 + 7=22>18$, $15 + 18 = 33>7$, $7 + 18 = 25>15$. So, it can be side - lengths of a triangle.

Step4: Check 9, 8, 10

$9 + 8=17>10$, $9 + 10 = 19>8$, $8 + 10 = 18>9$. So, it can be side - lengths of a triangle.

Step5: Check 7.8, 8.4, 16.2

$7.8+8.4 = 16.2$, which does not satisfy the triangle - inequality theorem (the sum should be strictly greater). So, it cannot be side - lengths of a triangle.

Answer:

4, 11, 9: Can be side lengths of a triangle
15, 7, 18: Can be side lengths of a triangle
9, 8, 10: Can be side lengths of a triangle
7.8, 8.4, 16.2: Cannot be side lengths of a triangle