triangel side length problem, difficult?

Question

The three sides of a triangle have lengths a, b, and c. All three lengths are whole numbers, and a

by that i mean, for example following the a for example, if c=3, following that rule only 4 possible triangles can be constructed,c=6 11 possible triangles can be constructed. What is the general law (formula) where you can input C to get the number of possible constructed triangles. Show how you got that

Answer 1

a2+b2=c2 Pathagoreom therom
okay you look at the a side... you take that number and you square it... (multiply it by itself)... then you take the b side and you square it... (multiply it by itself).. then you add both the totals together... (a and b's total) then that answer you write down and after it put =c2 then on the calculator type in that number and press the square root button.. and that's you answer then write it and after it write =c

and the total length of a triangle is 180

80, 80, and 100 a2+b2= c2
20 squared is 40, 20 squared is 40, 40+40=80 80 plus 100 is 180 c has to be longer than a and b because it is the hypotenuse.

Answer 2

For any value of c the following must hold true: a+b > c.

In words, this says that in any triangle the sum of any two sides must be greater than the third side. Euclid proved this over 2000 years ago.

Just try and make a triangle with sides 3, 4, and 9 and you will quickly see the truth of this theorem.