Two sides of a triangle measure 25 cm and 35 cm.Which could be the third side.
Well, my dear friend, let me give you a humorous answer. The third side of the triangle could be anything you desire! A unicorn riding a rainbow, a slice of pizza, or even a giant rubber duck! But in all seriousness, let's find the answer. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So, in this case, the third side could range anywhere from being 10 cm shorter than 35 cm (which is 25 cm) to being 10 cm longer than 25 cm (which is 35 cm). Therefore, the third side could be any length between 15 cm and 45 cm.
To determine the possible length of the third side of a triangle when two sides are given, you can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's apply this theorem to the given information:
Given:
- One side measures 25 cm
- Another side measures 35 cm
To find the possible length of the third side, we can consider two cases:
Case 1: Assuming the third side is the longest side:
In this case, the sum of the other two sides must be greater than the third side.
25 cm + 35 cm > x
60 cm > x
Therefore, the third side must be less than 60 cm for it to form a triangle.
Case 2: Assuming the third side is the shortest side:
In this case, the difference between the longest side and the other side must be less than the third side.
35 cm - 25 cm < x
10 cm < x
Therefore, the third side must be greater than 10 cm for it to form a triangle.
Based on the above analysis, the possible length of the third side falls within the range of 10 cm to 60 cm.
To determine the possible length of the third side of a triangle when the lengths of two sides are known, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
So, in this case, the sum of the two known sides (25 cm and 35 cm) must be greater than the length of the unknown third side. Mathematically, this can be expressed as:
25 cm + 35 cm > third side length
Simplifying this inequality:
60 cm > third side length
Therefore, the possible length of the third side must be less than 60 cm for it to be a valid triangle.
In conclusion, any length less than 60 cm could be the third side of the triangle.
The sum of any two sides must be greater than the third side
Let the third side be x
x+25 >35
x > 10
x+35 > 25
x > -10 , obviously!
25 + 35 >x
x < 60
so 10 < x < 60
So the third side could be any real number between 10 and 60