a triangle has two sides that have lengths of 14 feet and 22 feet. which of the following lengths could not represent the length of the third side...
A 8FT
B 12FT
C 14FT
D 20FT
22 - 14 = 8
To determine which length could not represent the length of the third side of the triangle, we can use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's check each option:
A) 8FT
14FT + 8FT = 22FT (Greater than the third side length)
8FT + 22FT = 30FT (Greater than the first side length)
The length of 8FT is possible.
B) 12FT
14FT + 12FT = 26FT (Greater than the third side length)
12FT + 22FT = 34FT (Greater than the first side length)
The length of 12FT is possible.
C) 14FT
14FT + 14FT = 28FT (Equal to the third side length)
14FT + 22FT = 36FT (Greater than the first side length)
The length of 14FT is also possible.
D) 20FT
14FT + 20FT = 34FT (Greater than the third side length)
20FT + 22FT = 42FT (Greater than the first side length)
The length of 20FT is possible as well.
Based on the triangle inequality theorem, all the given lengths could represent the length of the third side of the triangle. None of the options could not represent the length of the third side.
Therefore, the answer is none of the above.
To determine which length could not represent the length of the third side of the triangle, we should use the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the two given sides have lengths of 14 feet and 22 feet. Let's check each answer option:
A) 8 feet: To form a triangle, the sum of the two smaller sides must be greater than the third side. 14 + 8 = 22, which is equal to the third side of 22 feet. So option A could be the length of the third side.
B) 12 feet: Again, let's check if the sum of 14 and 12 is greater than 22. 14 + 12 = 26, which is greater than the third side of 22 feet. So option B could be the length of the third side.
C) 14 feet: This option is equal to one of the given side lengths, so it could be the length of the third side.
D) 20 feet: To form a triangle, the sum of the two smaller sides must be greater than the third side. 14 + 20 = 34, which is greater than the third side of 22 feet. So option D could also be the length of the third side.
In conclusion, all of the answer options (A, B, C, and D) could represent the length of the third side of the triangle.