Question

Determine if the given sides form a triangle.
7 ​m, 7 ​m, 14 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.
​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.
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 equal to the length of the third side.
D.
​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.

Answer 1

To determine if the given sides 7 m, 7 m, and 14 m can form a triangle, we use the triangle inequality theorem. This theorem states that for any three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Let's check the requirement for these sides:

1. The two shorter sides are 7 m and 7 m.
2. The length of the third side is 14 m.

Now, we calculate the sum of the two shorter sides:

\[ 7 + 7 = 14 \]

Now we compare this sum with the length of the third side:

\[ 14 \, \text{m} \text{ (the sum of the two shorter sides)} \]

Since \( 14 \, m = 14 \, m \), according to the triangle inequality theorem, the sum of the lengths of the two shorter sides is equal to the length of the third side. This means that these sides do not satisfy the strict inequality required to form a triangle.

Based on the choices provided, the correct answer is:

**D. No, because the sum of the lengths of the two shorter sides is 14 m, which is equal to the length of the third side.**