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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