Question

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

Answer 1

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.

Answer 2

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

Answer 3

c corret

Answer 4

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:

Answer 5

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

Answer 6

Oooh okay okay I get it

Answer 7

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

Answer 8

Haha yeah it is!

Answer 9

Thank's for your help!

Answer 10

You're welcome!

Answer 11

One more thing.

Answer 12

Yeahh..?

Answer 13

Like the ones that say <= ?

Answer 14

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.

Answer 15

Yes please!!

Answer 16

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.

Answer 17

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"

Answer 18

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

Answer 19

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

Answer 20

Yeah thank you!

Answer 21

You're welcome!

Answer 22

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