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Question

The sides of a triangle with positive area have lengths 4, 6 and x . The sides of a second triangle with positive area have length 4, 6 and y. The smallest positive number that is not the positive number that is not the possible value of | x - y | is ( x and y are integer )

A
2
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B
4
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C
6
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D
8
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Solution

The correct option is D 8
We have the fact that sum of lengths of 2 sides of a triangle is always greater than the 3rd side.
Let us take the minimum and maximum values of the third side as 'x' and 'y'
Minimum value is 64i.e2
Maximum value is 6+4i.e10
So, |xy||102|i.e8
The smallest positive number that is not the possible value of |x-y| is 8

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