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?

Correct result:

n =  7

Solution:

$$\begin{gathered} a=4\text{ cm } \\ b=9\text{ cm } \\ a<b+c \\ b<a+c \\ c<a+b \\ 4<9+c \\ 9<4+c \\ c<9+4 \\ c>5 \\ c<13 \\ 5<c<13 \\ c:6,7,8,9,10,11,12 \\ n=7 \end{gathered}$$

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