Greatest and least possible values of the sides of a triangle??

[cleocj1000]

In the figure of the triangle, side x is 7 and side y is 11. What is the difference between the greatest and least possible integer values of z?

 

[tkhunny]

What say you? What resources have you? Is there a "Triangle Inequality" in your collection of tools? How does one build a triangle, given only two sides?

 

[Dr.Peterson]

You can just imagine making two sticks with lengths 7 and 11 and attaching them at one end. Move them around in your mind. How would you place them to make the far ends as far apart as possible? As close to one another as possible? Now think about what z would be in each case.

The thinking involved here leads to the triangle inequality, but you don't have to formally use that unless you want to.

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