geometry inequality triangles help if you can
posted by Knights .
Two sides of an obtuse triangle are 16 and 21. How many possible lengths are there for the third side, if it is a positive integer?
i know that in an obtuse triangle
a^2+b^2<c^2
a+b>c
but i tried plugging in and it wont work so couldyou guys help me?
btw merry christmas and happy new year

First let's establish the domain for the third side
let the third side be c
c+16>21 > c > 5
c+21 > 16 > c > 5 , obviously
21 + 16 > c > c < 37
so to be a triangle in the third side must be
5 < c < 37
Now to be obtuse
c^2> 21^2+16^2
c^2 > 697
c > 26
could one of the other angles be obtuse ?
21^2 >c^2 + 16^2
c^2 < 185
c < 14
16^ > c^2 + 21^2
c^2 < a negative, which is not possible
So for the angle opposite the third side to be obtuse,
26 < c < 37
For the angle opposite the side 21 to be obtuse,
5 < c < 14 
thanks a lot the answer is 18 right?
merry christmas and happy new year to y 
No, 18 does not work.
Notice my two possible solutions, .....
So for the angle opposite the third side to be obtuse,
26 < c < 37
So the third side could be 27, 28, 29, 30 31 32 33 34 35 or 36
For the angle opposite the side 21 to be obtuse,
5 < c < 14
so the third side could be 6 7 8 9 10 11 12 or 13
make a sketch using one of the answers and illustrate that the angle must be obtuse by using the cosine law.
Also test it with your 18 to show it does not work 
I meant the total number of possibilities. Thanks anyway!

Eighteen is correct. I had the same problem and got it right
Respond to this Question
Similar Questions

Geometry REPOST
Please try to help me out as much as possible  this homework is due tomorrow. Thx :) <=angle T=perpendicular to (when upside down) (Write proof in twocolumn form) Given: <JMK=<LMK; segment MK T plane P Prove: segment JK … 
Geometry
1. The sides of a triangle have lenghts x, x+4, and 20. Specify those values of x for which the triangle is acute with the longest side 20. 2. use the information to decide if triangle ABC is acute, right, or obtuse. AC=13, BC= sq. … 
geometry
the sides of a triangle have lengths 4x+1, 2x+1 and 6x1. if the lengths of the longest side is 6x1, what values of x make the triangle obtuse? 
Math
If all of the following triangles have the same perimeter, which has the greater area? 
math problem triangle inequality help
Two sides of a triangle are 11 and 17. How many possible lengths are there for the third side, if it is a positive integer? 
Triangle inequality?
Two altitudes of a triangle have lengths 12 and 14. What is the longest possible length of the third altitude, if it is a positive integer? 
Math
The sum of the lengths of any two sides of a triangle must be greater than the third side. If a triangle has one side that is 22 cm and a second side that is 2 cm less than twice the third side, what are the possible lengths for the … 
Math
A triangle has side lengths 10, 15, and 7. Is the triangle acute, obtuse, or right? 
Geometry
Please check my answers 1. A triangle has side lengths of 34 in, 20 in, and 47 in. Is the triangle acute, obtuse or right? 
Math
Use the congruent triangles shown to answer question 6 and 7. 6. A. B. C. D. 7. Side BC is congruent to which side?