Question : The lengths of the three sides of a triangle are 30 cm, 42 cm, and $x$ cm. Which of the following is correct?
Option 1: $12 \leq x<72$
Option 2: $12>x>72$
Option 3: $12<x<72$
Option 4: $12 \leq x \leq 72$
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Correct Answer: $12<x<72$
Solution : The sum of the lengths of any two sides of a triangle is greater than the third side. Also, the difference in lengths of any two sides of a triangle is smaller than the third side. According to the question, $(30+42)>x>(42-30)$ ⇒ $72>x>12$ ⇒ $12<x<72$. Hence the correct answer is $12<x<72$.
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