Question
If you form a triangle from three given side lengths, will you always get one triangle or more than one triangle?
Question content area bottom
Part 1
Choose the correct answer below.
A.
You will always get more than one triangle.
B.
You will always get one triangle, as long as the sum of the lengths of any two sides is greater than the length of the third side.
C.
You will always get one triangle, as long as the sum of the lengths of any two sides is less than or equal to the length of the third side.
D.
You will always get two triangles, as long as the sum of the lengths of any two sides is greater than the length of the third side.
Question content area bottom
Part 1
Choose the correct answer below.
A.
You will always get more than one triangle.
B.
You will always get one triangle, as long as the sum of the lengths of any two sides is greater than the length of the third side.
C.
You will always get one triangle, as long as the sum of the lengths of any two sides is less than or equal to the length of the third side.
D.
You will always get two triangles, as long as the sum of the lengths of any two sides is greater than the length of the third side.
Answers
Answered by
GPT-4o mini
The correct answer is:
**B. You will always get one triangle, as long as the sum of the lengths of any two sides is greater than the length of the third side.**
According to the triangle inequality theorem, for three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If this condition is satisfied, exactly one triangle can be formed with those side lengths. If the condition is not satisfied, no triangle can be formed. There are specific cases where two different triangles can be formed with two sides of equal lengths and a variable length that can fit within a certain range, but generally, for given three side lengths, if they satisfy the triangle inequality, there is only one triangle.
**B. You will always get one triangle, as long as the sum of the lengths of any two sides is greater than the length of the third side.**
According to the triangle inequality theorem, for three lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If this condition is satisfied, exactly one triangle can be formed with those side lengths. If the condition is not satisfied, no triangle can be formed. There are specific cases where two different triangles can be formed with two sides of equal lengths and a variable length that can fit within a certain range, but generally, for given three side lengths, if they satisfy the triangle inequality, there is only one triangle.
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