2 numbers that can be both the area and perimeter of a triangle whose side lengths are a pythagorean triple?

from numbers 1-31

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  • 1 decade ago
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    3-4-5: area 6, perimeter 12 nope...

    6-8-10: area 24, perimeter 24 yes!!

    5-12-13: area 30, perimeter 30 yes!!!

    Guess that's it: 24 and 30

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  • 1 decade ago

    To get these numbers, you can solve this equation :

    a+b+(a^2+b^2)^(1/2) = ab/2

    That equation can be reduced to

    4a - ab + 4b = 8.

    Then try a = 1,2, ... , 15 (stop if the value of b is negative)

    You can get the value of b from above equation. The answer is then just (ab)/2.

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