# Triangles

Hanka cut the 20 cm long straws into three pieces each piece had a length in cm. Then, with these three pieces, she tried to make a triangle.

a) What circuit has each of the triangles?
b) How long can the longest side measure?
c) How many different triangles could be made?

Result

o =  20 cm
a =  9 cm
n =  8

#### Solution:

$o=20 \ \text{cm}$
$a+b+c=20 \ \\ a < b+c \ \\ 9 < 9 + 2 \ \\ a=9 \ \text{cm}$
$2,9,9 \ \\ 3,8,9 \ \\ 4,7,9 \ \\ 4,8,8 \ \\ 5,6,9 \ \\ 5,7,8 \ \\ 6,6,8 \ \\ 6,7,7 \ \\ \ \\ n=8$

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