If two sides of a triangle are 6 and 25.?

Question

If two sides of a triangle are 6 and 25, what is the range of possibilities for the third side?

1. 19<x<31

2. 6<x<25

3. 14<x<16

4. 11<x<20

Answer 1

1. 19&lt;x&lt;31

Think of it as if you had 2 sticks, one 6 and the other 25.  If you were to lay them next to each other with the end of one stick flush with the end of the other, the short stick would be 19 short of being able to touch the other end of the other stick.  Just touching wouldn&#039;t make it a triangle either and so that&#039;s why a &lt; than symbol is used rather then a greater than or equal to.  Any amount longer than 19 (however small) will make a triangle.

On the other extreme, if the 2 sticks were end to end they would be 31 long.  The third piece would have to be smaller than that (even it was only 30.9999999999999999999999), to have a triangle.  

Those are the extreme cases, thus defining the range.

Answer 2

1. 19&lt;x&lt;31

Any two sides of a triangle have to add up to be greater than the 3rd side =)