Determine if the given sides form a triangle.
3.9 m, 1.9 m, 0.4 m
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 ___ m, which is equal to the length of the third side.
B. Yes, because the sum of the lengths of the two shorter sides is ___ m, which is greater than the length of the third side.
C. Yes, because the sum of the lengths of the two shorter sides is ___ 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 ___ m, which is less than the length of the third side.
To determine if the given sides (3.9 m, 1.9 m, and 0.4 m) can form a triangle, we can use the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.
First, let’s identify the two shorter sides and the longest side:
– Shorter sides: 1.9 m and 0.4 m
– Longest side: 3.9 m
Now we calculate the sum of the two shorter sides:
1.9 m + 0.4 m = 2.3 m
Now we compare this sum with the longest side:
– The longest side is 3.9 m.
Since 2.3 m (the sum of the two shorter sides) is less than 3.9 m, the condition for forming a triangle is not satisfied.
Therefore, the correct choice is:
D. No, because the sum of the lengths of the two shorter sides is 2.3 m, which is less than the length of the third side.