Drag each set of side lengths to show whether they can or cannot make a triangle, or if there is not enough information to tell.
Options:
CAN Make a Triangle
CANNOT Make a Triangle
Not Enough Information
Choices:
5 ft, 7 ft, 11 ft
5 ft, 9 ft, 14 ft
4 ft, 6 ft, 11 ft
7 ft, 8 ft, 14 ft
(Can someone please clarify HOW to solve this??)
Based on the basic property that
to gave a valid triangle, the sum of any two sides must be greater than the third side.
I will test the last one, you do the others.
7 ft, 8 ft, 14 ft
7+8>14, yes
7+14>8 , yes
8+14>7, yes
So, this triangle exists
Can you please check D
To determine whether a triangle can be formed with a set of side lengths, we need to apply the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's go through each set of side lengths one by one:
1. 5 ft, 7 ft, 11 ft:
To check if a triangle can be formed, we need to compare the sum of any two sides with the length of the remaining side.
5 ft + 7 ft = 12 ft (less than 11 ft)
5 ft + 11 ft = 16 ft (greater than 7 ft)
7 ft + 11 ft = 18 ft (greater than 5 ft)
Since the sum of any two sides is greater than the length of the remaining side, this set of side lengths can form a triangle.
2. 5 ft, 9 ft, 14 ft:
5 ft + 9 ft = 14 ft (equal to 14 ft)
5 ft + 14 ft = 19 ft (greater than 9 ft)
9 ft + 14 ft = 23 ft (greater than 5 ft)
Since the sum of any two sides is greater than the length of the remaining side, this set of side lengths can form a triangle.
3. 4 ft, 6 ft, 11 ft:
4 ft + 6 ft = 10 ft (less than 11 ft)
4 ft + 11 ft = 15 ft (greater than 6 ft)
6 ft + 11 ft = 17 ft (greater than 4 ft)
Since the sum of any two sides is greater than the length of the remaining side, this set of side lengths can form a triangle.
4. 7 ft, 8 ft, 14 ft:
7 ft + 8 ft = 15 ft (greater than 14 ft)
7 ft + 14 ft = 21 ft (greater than 8 ft)
8 ft + 14 ft = 22 ft (greater than 7 ft)
Since the sum of any two sides is greater than the length of the remaining side, this set of side lengths can form a triangle.
Therefore, the answers are:
1. CAN Make a Triangle
2. CAN Make a Triangle
3. CAN Make a Triangle
4. CAN Make a Triangle