The lengths of the sides of a triangle are 17, 8, and n. Which of the following must be true?

Question

ayyookyndall · Answer

a. 9 < n < 25
b. n > 25
c. n <9
d. 9 < n < 25

ayyookyndall · Answer

b and d both have a _ under<

anonymous · Answer

B

ayyookyndall · Answer

Can you explain this to me @jim_thompson5910 @Reaper534 @Mesopretty

anonymous · Answer

In order for these to be sides of a triangle, any two sides added together must be greater than the remaining side. 

8 + 9 > 17 
17 > 17 
Not true, so it isn't a triangle. 

9 + 9 > 17 
18 > 17 
True so far . . . 
9 + 17 > 9 
26 > 9 
True, so it is a triangle 

8 + 13 > 23 
21 > 23 
Not true, not a triangle 

13 + 9 > 23 
22 > 23 
Not true, not a triangle 

Only the second one (9, 9 and 17) could be sides of a triangle.

anonymous · Answer

This is an example

jim_thompson5910 · Answer

In general, if we have a triangle with the three sides a,b,c

|dw:1417737792766:dw|

The side c is restricted by this compound inequality

$$\Large a-b < c < a+b$$

where $a \ge b$

ayyookyndall · Answer

So B?

ayyookyndall · Answer

Or D?

ayyookyndall · Answer

Both of them look like they would work @jim_thompson5910

jim_thompson5910 · Answer

Let

a = 17
b = 8
c = n

|dw:1417737941694:dw|

jim_thompson5910 · Answer

then use 

$$\Large a-b < c < a+b$$

ayyookyndall · Answer

9 < c < 25
So its between A and D

What about the _ under this <

@jim_thompson5910

anonymous · Answer

Acually it is A