Determine whether the following lengths can make a triangle: 3, 5, 7
To determine whether the given lengths can make a triangle, we need to apply the triangle inequality theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, we have the lengths 3, 5, and 7. Let's check if the triangle inequality holds:
1. The sum of the lengths of sides 3 and 5 is: 3 + 5 = 8
Is 8 greater than 7? Yes.
2. The sum of the lengths of sides 3 and 7 is: 3 + 7 = 10
Is 10 greater than 5? Yes.
3. The sum of the lengths of sides 5 and 7 is: 5 + 7 = 12
Is 12 greater than 3? Yes.
Since the sum of any two sides is always greater than the third side, we can conclude that a triangle can be formed with side lengths 3, 5, and 7.