Question 118100: Myia is running for student council president and wants to design a campaign button that is triangular. None of the sides can measure more than 7 centimeters. How many different triangular buttons are possible assuming all the sides are whole centimeters?
Is there a patttern that might help solve the problem?
Ofthe possible lengths of three sides, which one generates a triangle?
Which triangle would be recommended to be used for the campaign buton?
Draw all possible triangles?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Ideas to consider.
1.Each of the three sides must be 1 or 2 or 3 ... or 7
2.There are 7*7*7 = 343 such patterns of side lengths.
3.Only those patterns where the sum of each pair of sides
is greater than the third side will form a triangle.
For example 1,2,7 cannot form a triangle.
4. Getting started
Let one side be 7 and figure out what the other sides must
be:
(7,1,7)-----no others starting with (7,1
(7,2,7),(7,2,6) ----no others starting with (7,2
(7,3,7),(7,3,6),(7,3,5)---no others starting with (7,3
etc.
Follow some pattern of development, without duplicating, till you
have all the possible patterns listed.
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Cheers,
Stan H.
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