Answer:
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
Explanation:
There is an important rule about the sides of the triangle
- The sum of lengths of the smallest two sides of a triangle must be greater than the length of the third side
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