## babybri_ 2 years ago If r = 17.2 mm and p = 10.4 mm, which of the following is the range that represents a possible length for q in this triangle? A) 6.8 mm < q < 27.6 mm B) q >= 6.8 mm C) 6.8 mm <= q <= 27.6 mm D)q <= 27.6 mm

1. tcarroll010

In a triangle, the measure (length) of no one side can be equal to or greater than the sum of the measures of the other 2 sides. So, look for an expression where "q" does not go over a certain value.

2. babybri_

I'm sorry lol I'm a little confused..

3. jishan

c corret

4. tcarroll010

|dw:1355068873536:dw|np, if you have 2 sides that are 5 and 7, then the third side has to be less than 5 + 7 or 12, because you would have something like this otherwise:

5. tcarroll010

And in that case, you would see that the 2 shortest sides could never connect.

6. babybri_

Oooh okay okay I get it

7. tcarroll010

This is one of those "a picture says a thousand words" problems!

8. babybri_

Haha yeah it is!

9. babybri_

10. tcarroll010

You're welcome!

11. tcarroll010

One more thing.

12. babybri_

Yeahh..?

13. babybri_

Like the ones that say <= ?

14. tcarroll010

Actually, I just saw the correct answer. It is indeed listed correctly. But it is a little tricky, so I'll stick around if you want to try it out.

15. babybri_

16. tcarroll010

Definitely. Here's a hint: that relationship that I described above has to hold for all 3 types. That is: p < q + r q < p + r r < p + q So, that is the trick. All 3 relationships have to be satisfied.

17. tcarroll010

One more hint: 2 of the selections look very similar and it will be the one with the inequalities in it, not the mixed "inequality with equality"

18. tcarroll010

So, back to my example of where you have 2 sides where one is 5 and one is 7. The third side has to be shorter than 12, but it also has to longer than 2 2 < third side < 12 because if it is longer than (or equal to) 12, then it is greater than (or =) 5 + 7 if it is shorter than (or =) 2, then 7 is greater than (or =) 5 + the third side

19. tcarroll010

So, with this information, are you able to get the correct range now?

20. babybri_

Yeah thank you!

21. tcarroll010

You're welcome!

22. phi

one way to see the answer: hook together r = 17.2 mm and p = 10.4 mm with a hinge. if you close them, you get the shortest possible 3rd side if you open them into a line, you get the longest possible 3rd side |dw:1355073170590:dw|