If two sides of a triangle are 6 cm, and 14cm. What are the limiting values of the third side?
Answer: 8 < x < 20
Explanation
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.
Let the third side be x.
Given sides: 6 cm and 14 cm
The third side x must satisfy:
1. x + 6 > 14 => x > 8
2. x + 14 > 6 => x > -8 (this is always true since x is positive)
3. 6 + 14 > x => x < 20
Combining these conditions:
8 < x < 20
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