Apply the Triangle Inequality Theorem to determine whether sides with lengths of 5 inches, 10 inches, and 15 inches form a triangle.(1 point)
Responses
Yes, because the sum of 5+10 is less than or equal to 15.
Yes, because the sum of 5 plus 10 is less than or equal to 15.
Yes, because the sum of 5+10 is not greater than 15.
Yes, because the sum of 5 plus 10 is not greater than 15.
Yes, the majority of the conditions are met.
Yes, the majority of the conditions are met.
No, because the sum of 5+10 is not greater than 15.
No, because the sum of 5 and 10 is not greater than 15.
No, because the sum of 5 + 10 is not greater than 15.
To determine whether the given lengths of 5 inches, 10 inches, and 15 inches form a triangle, we can apply the Triangle Inequality Theorem.
According to the Triangle Inequality Theorem, for a triangle to be formed, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check if this condition is met with the given lengths:
1. Sum of 5 inches + 10 inches = 15 inches.
2. Compare this sum with the length of the third side, which is 15 inches.
In this case, the sum of the first two sides, 5 inches and 10 inches, is equal to the length of the third side, 15 inches.
Therefore, the sum of any two sides is not greater than the length of the third side.
Based on this, the correct response is:
No, because the sum of 5+10 is not greater than 15.