Question

Which of the following could not be a value of n?

A. 7
B. 10
C. 13
D. 22

Answer 1

Triangle inequality :)
Here's a direct approach... if you're given two sides of a triangle, say, a and b, the third side MUST fall within this (open) interval:
\[\Large (|a-b| \ , \ a+b)\]

Answer 2

In this case, your a and b (it doesn't really matter which is which) are 13 and 9.

What's the interval?

Answer 3

im not sure. =/

Answer 4

Okay, your a is 13, your b is 9.

What is |a - b| ?

Answer 5

4

Answer 6

that's right :)
Now what's a+b?

Answer 7

22!

Answer 8

That's right :)
So, the possible values for n (the third side)
must be STRICTLY between
4 and 22.

One of these choices... isn't :D

Answer 9

Which is it?

Answer 10

22 !?

Answer 11

Yes. 22 is not STRICTLY between 4 and 22.
So that's the impossible value for n :D

Answer 12

ahh. thank you so much! i appreciate it when people walk me through it! i typed the whole equation in a calculator, and it didnt come up right, so i had to question it before you explained it further. thank you so much!!

Answer 13

No problem :)