For 4-6, determine whether the three numbers could be the lengths of the sides of a triangle.
4. 4, 8, 11
5. 6, 12,5
6. 13, 13, 26

4. 4, 8, 11 could be the lengths of the sides of a  triangle

5. 6, 12, 5 could not be the lengths of the sides of a  triangle

6. 13, 13, 26 could not be the lengths of the sides of a  triangle

Step-by-step explanation:

There is an important rule about the sides of the triangle

Let us use this rule to solve questions 4, 5, and 6

#4.

∵ The numbers are 4, 8, 11

∵ The two smallest numbers are 4, 8

∵ Their sum = 4 + 8 = 12

∵ The greatest number is 11

∵ 12 > 11

∴ The sum of the two smallest number is greater than the third number

∴ The numbers could be the length of the sides of a triangle

∴ 4, 8, 11 could be the lengths of the sides of a  triangle

#5.

∵ The numbers are 6, 12, 5

∵ The two smallest numbers are 5, 6

∵ Their sum = 5 + 6 = 11

∵ The greatest number is 12

∵ 11 < 12

∴ The sum of the two smallest number is smaller than the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 6, 12, 5 could not be the lengths of the sides of a  triangle

#6.

∵ The numbers are 13, 13, 26

∵ The two smallest numbers are 13, 13

∵ Their sum = 13 + 13 = 26

∵ The greatest number is 26

∵ 26 = 26

∴ The sum of the two smallest number is equal to the third number

∴ The numbers could not be the length of the sides of a triangle

∴ 13, 13, 26 could not be the lengths of the sides of a  triangle