G-3 Triangles of the year

Geometry Level 4

How many triangles of different integral length of sides are there with perimeter 2016?


The answer is 84169.

Brian Dela Torre by Brian Dela Torre , 21, Philippines

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1 solution

Brian Dela Torre
Jan 29, 2016

Since we find the number of scalene triangle. We use the formula for even perimeters which is...

( P − 6 ) 2 48 \frac{ (P - 6)^{2} }{ 48 }

We came up with 84168.75 rounding up to the nearest integer 84169 \boxed{84169}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

How do you know it came up to be (P-6)^2 /48?

Pi Han Goh - 5 years, 4 months ago

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@Pi Han Goh Sir, you may want to have a look at this paper .....

Aaghaz Mahajan - 2 years, 2 months ago

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