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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