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Why do some lengths not form a triangle?
Some lengths do not form a triangle due to 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. If this condition is not met for any combination of the sides, the lengths cannot create a closed figure, resulting in no triangle. For example, if one side is longer than the sum of the other two, the sides will not connect to form a triangle.
Could 4 7 7 be side lengths of a triangle?
Yes and the given lengths would form an isosceles triangle.
Why do some lengths form a triangle and some don't?
The ability for three lengths to form a triangle is determined by 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. If this condition is not met, the lengths cannot connect to form a closed shape, resulting in an invalid triangle. For example, lengths of 3, 4, and 5 can form a triangle because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3. Conversely, lengths like 2, 2, and 5 cannot form a triangle because 2 + 2 is not greater than 5.
What is the area of a triangle with the side lengths of 2 12 and 18?
These dimensions do not form a triangle.
Can the segment lengths 9 4 15 form a triangle?
No.
Why do some lengths not form a triangle?
Some lengths do not form a triangle due to 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. If this condition is not met for any combination of the sides, the lengths cannot create a closed figure, resulting in no triangle. For example, if one side is longer than the sum of the other two, the sides will not connect to form a triangle.
Could 4 7 7 be side lengths of a triangle?
Yes and the given lengths would form an isosceles triangle.
Why do some lengths form a triangle and some don't?
The ability for three lengths to form a triangle is determined by 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. If this condition is not met, the lengths cannot connect to form a closed shape, resulting in an invalid triangle. For example, lengths of 3, 4, and 5 can form a triangle because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3. Conversely, lengths like 2, 2, and 5 cannot form a triangle because 2 + 2 is not greater than 5.
What is the area of a triangle with the side lengths of 2 12 and 18?
These dimensions do not form a triangle.
Is it possible to form a triangle with the lengths of 1 8 and 8?
Sure! It will be an isosceles triangle.
Can the segment lengths 9 4 15 form a triangle?
No.
Can you form a triangle with lengths of 8 8 and 1?
Yes.
Which set of side lengths cannot form a triangle?
1.5m
Can the lengths 7 and 1 and 7 form a triangle?
Yes and it will be in the form of an isosceles triangle having two equal sides.
What is the sum of the lengths of any two sides of a triangle is greater than the length of the third side?
The statement that the sum of the lengths of any two sides of a triangle is greater than the length of the third side is known as the Triangle Inequality Theorem. This theorem is fundamental in geometry and ensures that a set of three lengths can form a triangle. If this condition is violated, the three lengths cannot connect to form a triangle. Essentially, it guarantees the triangle's stability and shape.
Can the following side lengths form a triangle 3 8 3?
Yes, an isosceles triangle with two size lengths of 3 and one of 8 :)
When do three side lengths measures form a triangle?
Three side lengths can form a triangle if they satisfy 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. This must hold true for all three combinations of the side lengths. For example, if the side lengths are (a), (b), and (c), then (a + b > c), (a + c > b), and (b + c > a) must all be true. If any of these conditions are not met, the side lengths cannot form a triangle.
