question_answer 12)

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

Answer:

                Let \[x\text{ }cm\] be the length of the third side. \[\because \]     Sum of the lengths of any two sides of a triangle is greater than the length of the   third side. \[\therefore \] We should have \[12+15>x\]\[\Rightarrow \] \[27>x\Rightarrow x<27\] \[15+x>12\] \[\Rightarrow \] \[x>12-15\Rightarrow x>-3\] \[x+12>15\] \[\Rightarrow \]      \[x>15-12\Rightarrow x>3\] \[x>-3\]and \[x>3\] \[\Rightarrow \] \[x>3\] \[\therefore \]  The length of the third side should be any length between 3 cm and 27 cm.