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Answer :
Lillian can construct a triangle because the sum of any two sides is greater than the third side.
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Rewritten by : Barada
"The correct statement to explain whether Lillian is correct is: Lillian can construct a triangle from the given rods because the sum of the lengths of the two shorter rods is greater than the length of the longest rod, satisfying the triangle inequality theorem.
To determine if Lillian can construct a triangle from the rods with lengths 12 inches, 36 inches, and 39.4 inches, we must apply the triangle inequality theorem. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.
Let's denote the lengths of the rods as follows:
- a = 12 inches
- b = 36 inches
- c = 39.4 inches
According to the triangle inequality theorem, the following inequalities must be satisfied for the rods to form a triangle:
1. a + b > c
2. a + c > b
3. b + c > a
Now, let's check each inequality:
1. a + b = 12 + 36 = 48 inches, which is indeed greater than c = 39.4 inches.
2. a + c = 12 + 39.4 = 51.4 inches, which is greater than b = 36 inches.
3. b + c = 36 + 39.4 = 75.4 inches, which is greater than a = 12 inches.
Since all three inequalities are satisfied, Lillian is correct in claiming that she can construct a triangle from the given rods."
