Question

A triangle has sides of lengths 12-x,12 and 12+x. What are all of the possible integer values for x?

Answer 1

Can x be 12?

Answer 2

Each side must less than the sum of two others and bigger than their difference

Answer 3

Let us try x=6, we get 6,12,18. That is not possible since 8=6+12

Answer 4

Try to apply this to find what restriction you should have about x

Answer 5

By this I mean
Each side must less than the sum of two others and bigger than their difference

Answer 6

For example x=0 can work, you will get 12,12,12 and equilateral triangle.
You should find the general restriction. I am trying by my exmaples that some x's work and spme dp not

Answer 7

ok thank you

Answer 8

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Answer 9

Let me show you why x must be less than 6
(12+x) -(12-x) < 12 < 12+x +12-x
2 x < 12 <24
x<6