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=7a=4 \ \text{cm} \ \\ b=9 \ \text{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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