Question : The three sides of a triangle are 5 cm, 9 cm, and x cm. The minimum integral value of x is:
Option 1: 2
Option 2: 3
Option 3: 4
Option 4: 5
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Correct Answer: 5
Solution : Given: The three sides of a triangle are 5 cm, 9 cm, and $x$ cm. We know, the sum of two sides of a triangle is greater than the third side. So, $x$ < 5 + 9 ⇒ $x$ < 14 Again, we know the difference between the two sides of a triangle is less than the third side. So, $x$ > 9 – 5 ⇒ $x$ > 4 $\therefore$ 4 < $x$ < 14 So, the minimum value of x is 5. Hence, the correct answer is 5.
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