Question 362234: How many triangles can you make if their perimeter can only be 24 units? The demensions are only in whole numbers. The triangles can be scalene, equilateral, or isocoles.
Answer by robertb(5830)   (Show Source):
You can put this solution on YOUR website! let x,y,z be the measures of the sides of the triangle. Then x+y+z = 24. By the symmetries of the triangle inequality,
x+y>z,
x+z> y,
y+z>x.
Using the the perimeter equation above and the 3 inequalities we arrive at
12>x, 12>y, 12>z.
By brute-force method, the following are the possible combinations:
(8,8,8) (7,6,11)
(7,8,9) (9,6,9)
(6,10,8) (9,5,10)
(5,11,8) (9,4,11)
(7,10,7) (4,10,10)
(3,10,11) (2,11,11)
therefore there are 12 possible traingles with perimeter 24 and integer sides.
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