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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.


what- Triangle rigidity means that a triangle cannot be deformed without changing its?

side lengths


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 triangle measures 2m 4m and 7m?

The triangle with side lengths of 2m, 4m, and 7m does not form a valid triangle. In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side according to the Triangle Inequality Theorem. In this case, 2m + 4m is less than 7m, violating the theorem. Therefore, a triangle with these side lengths cannot exist in Euclidean geometry.


Why can't you construct a ABC triangle?

You cannot construct a triangle ABC if the lengths of the sides do not 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. For example, if the side lengths are 2, 3, and 6, then 2 + 3 is not greater than 6, making it impossible to form a triangle. Additionally, if any side length is zero or negative, a triangle cannot be formed.


Can 4m 5m 7m side lengths form a Right triangle?

To determine if the side lengths of 4m, 5m, and 7m can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides. Here, 7m is the longest side. Calculating, (4^2 + 5^2 = 16 + 25 = 41) and (7^2 = 49). Since (41 \neq 49), these side lengths cannot form a right triangle.


Could 4 7 7 be side lengths of a triangle?

Yes and the given lengths would form an isosceles triangle.


What is the area of a triangle with the side lengths of 2 12 and 18?

These dimensions do not form a triangle.


How do you classify a triangle with 3 given side lengths?

That depends on what the side lengths are. Until the side lengths are known, the triangle can only be classified as a triangle.


Is it possible to form a triangle from the lengths 2cm 2cm 5cm?

No. It is not possible, because a triangle cannot have a side longer than the sum of two other sides. 5 is greater than 2+2. Therefore the triangle cannot exist.


Can segments 8 7 and 15 form a triangle?

To determine if segments of lengths 8, 7, and 15 can form a triangle, we can use 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. Here, 8 + 7 = 15, which is not greater than 15. Therefore, segments of lengths 8, 7, and 15 cannot form a triangle.


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 :)