how do I prove that 3,3,5 could represent the lengths of a triangle?
A basic property of any triangle is that the sum of any two sides must be greater than the third side.
so...
3+3>5
5+3>3
yes.
Thank you Reiny!
To prove that 3, 3, 5 can represent the lengths of a triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
In this case, let's consider the three sides to be 3, 3, and 5.
First, we need to determine the sum of the two shortest sides. In this case, both sides are 3. So, 3 + 3 = 6.
Now, we compare the sum to the length of the longest side, which is 5. Since 6 is greater than 5, the triangle inequality theorem is satisfied.
Therefore, we can conclude that 3, 3, 5 can represent the lengths of a triangle.