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Q.

Which of the following conditions would give us the third side of a triangle, if the other two sides of a triangle are 2 and 5 units respectively?

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a

3<x<7

b

2<x<7

c

3<x>7

d

3>x<7

answer is D.

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Detailed Solution

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The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.
Therefore, 5−2<x<5+2
3<x<7 is the possible length of the third side of a triangle.
For checking the possible length: Take 2,5,4
2+5>4(a + b>c)
5+4>2(b + c>a)
2+4>5(a + c>b)
Hence, the above condition satisfied the triangle inequality theorem.


 

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