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 not greater than 15.
Yes, because the sum of 5 plus 10 is not greater than 15.
No, because the sum of 5+10 is not greater than 15.
No, because the sum of 5 plus 10 is not greater than 15.
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, the majority of the conditions are met.
No, because the sum of 5+10 is not greater than 15.
To determine whether sides with lengths of 5 inches, 10 inches, and 15 inches form a triangle, we can apply the Triangle Inequality Theorem.
The Triangle Inequality 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.
So, in this case, we need to check if the sum of 5 inches and 10 inches is greater than 15 inches, and if the sum of 5 inches and 15 inches is greater than 10 inches.
To calculate these sums:
- 5 + 10 = 15
- 5 + 15 = 20
Comparing these sums to the length of the third side, which is 15 inches, we can see that 15 is not greater than 15.
Therefore, the sum of the lengths of any two sides is not greater than the length of the third side, and thus, these side lengths (5 inches, 10 inches, and 15 inches) do not form a triangle.
So the correct response is:
No, because the sum of 5+10 is not greater than 15.