2 numbers that can be both the area and perimeter of a triangle whose side lengths are a pythagorean triple?
from numbers 1-31
- Jim BurnellLv 61 decade agoFavorite Answer
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
- 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.