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 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
 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

This Question is Closed

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0In 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.

babybri_
 2 years ago
Best ResponseYou've already chosen the best response.0I'm sorry lol I'm a little confused..

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1355068873536:dwnp, 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:

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0And in that case, you would see that the 2 shortest sides could never connect.

babybri_
 2 years ago
Best ResponseYou've already chosen the best response.0Oooh okay okay I get it

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0This is one of those "a picture says a thousand words" problems!

babybri_
 2 years ago
Best ResponseYou've already chosen the best response.0Thank's for your help!

babybri_
 2 years ago
Best ResponseYou've already chosen the best response.0Like the ones that say <= ?

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0Actually, 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.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0Definitely. 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.

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0One 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"

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0So, 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

tcarroll010
 2 years ago
Best ResponseYou've already chosen the best response.0So, with this information, are you able to get the correct range now?

phi
 2 years ago
Best ResponseYou've already chosen the best response.0one 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
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