Triangles

Ivo wants to draw all the triangles whose two sides of which have a length of 4 cm and 9 cm and the length of the third side is expressed in whole centimeters. How many triangles does he have?

Result

n =  7

Solution:

$a = 4 \ cm \ \\ b = 9 \ cm \ \\ \ \\ a < b+c \ \\ b < a+c \ \\ c < a+b \ \\ \ \\ 4 < 9+c \ \\ 9 < 4+c \ \\ c < 9+4 \ \\ \ \\ c > 5 \ \\ c < 13 \ \\ \ \\ 5 < c < 13 \ \\ \ \\ c: 6,7,8,9,10,11,12 \ \\ \ \\ n = 7$

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