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Determine if the given sides form a triangle.

9 ​m, 9 ​m, 18 m
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Part 1
Select the correct choice​ below, and fill in the answer box to complete your choice.
​(Type an integer or a​ decimal.)
A.
​No, because the sum of the lengths of the two shorter sides is
  
enter your response here ​m, which is equal to the length of the third side.
B.
​No, because the sum of the lengths of the two shorter sides is
  
enter your response here ​m, which is less than the length of the third side.
C.
​Yes, because the sum of the lengths of the two shorter sides is
  
enter your response here ​m, which is greater than the length of the third side.
D.
​Yes, because the sum of the lengths of the two shorter sides is
  
enter your response here ​m, which is equal to the length of the third side.

1 answer

To determine if the given sides can form a triangle, we can use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Let's denote the sides as follows:

  • Side a = 9 m
  • Side b = 9 m
  • Side c = 18 m

Now we will check the sum of the lengths of the two shorter sides compared to the length of the third side:

  1. \( a + b = 9 m + 9 m = 18 m \)

Now, we compare this sum with the length of the third side (c):

  • The sum of the two shorter sides (18 m) is equal to the length of the third side (18 m).

According to the triangle inequality theorem, for three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Since in this case, the sum is equal to the third side, these lengths do not satisfy the condition.

Thus, the correct choice is:

A. No, because the sum of the lengths of the two shorter sides is 18 m, which is equal to the length of the third side.