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I was wondering if there is a formula that could generate the values of the sides of a triangle where his area equals to his perimeter. I only found that if the triangle is equilateral then $$l=\frac{12}{√3}$$ where $l$ is the side of the triangle.

Thanks for support

Peterix

P.S. There is a similar problem here

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1 Answer 1

Let $S$ be the area of a triancle. Let $P$ be the perimeter of a triancle. Let $r$ be the inscribed circle radius of a triangle.

Since $S=\frac12 r P$ we have $r=2.$ It gives us information for certain types of triangles. for exemples. For a right triangle we have $$r=\frac{a+b-c}{2}=2$$ Since $$c^2=a^2+b^2$$ we have $$a+b=2+\frac{ab}{4}$$

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Can you please tell me what are S,P and r? –  Peterix Jan 25 at 21:52
    
@Peterix I edited my answer –  nadia-liza Jan 25 at 22:00
    
Thanks a lot for help! –  Peterix Jan 25 at 22:04

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