Question : The three sides of a triangle are 9, 24, and S units. Which of the following is correct?
Option 1: $15 < S < 33$
Option 2: $15 \leq S<33$
Option 3: $15<S\leq 33$
Option 4: $15 \leq S \leq 33$
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Correct Answer: $15 < S < 33$
Solution : It is a property of a triangle that the sum of the lengths of any two sides of a triangle is always greater than the length of the third side. So according to the question : $\therefore$ 9 + 24 > S ⇒ S < 33 Also 24 – 9 < S ⇒ S < 15 $\therefore$ 15 < S < 33 Hence, the correct answer is $15<S<33$.
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