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
• B. 4
• C. 6
• D. 8

Answer 1

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 $\ge 6-4i.e\ge 2$

Maximum value is $\le 6+4i.e\le 10$

So, $|x-y|\le |10-2|i.e\le 8$

The smallest positive number that is not the possible value of |x-y| is 8