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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